diff options
Diffstat (limited to 'src/code/sys_math3d.c')
| -rw-r--r-- | src/code/sys_math3d.c | 2653 |
1 files changed, 2464 insertions, 189 deletions
diff --git a/src/code/sys_math3d.c b/src/code/sys_math3d.c index 45b94d569..ad617e50f 100644 --- a/src/code/sys_math3d.c +++ b/src/code/sys_math3d.c @@ -1,189 +1,2464 @@ -#include "global.h" - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_Normalize.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_PlaneVsLineSegClosestPoint.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_80179798.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_80179A44.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_80179B34.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_80179B94.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_80179D74.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ScaleAndAdd.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_Lerp.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_Parallel.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_AngleBetweenVectors.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_80179F64.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XZBoundCheck.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A09C.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A1D0.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A304.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A438.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XZLengthSquared.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XZLength.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XZDistanceSquared.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XZDistance.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_LengthSquared.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_Vec3fMagnitude.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_Vec3fDistSq.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_Distance.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_DistanceS.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A7B8.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A7F8.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017A838.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_CrossProduct.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_SurfaceNorm.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_PointRelativeToCubeFaces.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_PointRelativeToCubeEdges.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_PointRelativeToCubeVertices.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_LineVsCube.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017B68C.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017B7F8.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_UnitNormalVector.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_SignedDistanceFromPlane.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017B9D8.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_UDistPlaneToPos.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_DistPlaneToPos.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaYDist.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017BD98.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017BDE0.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaYIntersectDist.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaYIntersectInsideTri.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017BF8C.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkLineSegParaYIntersect.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017C17C.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017C1F0.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaYIntersectInsideTri2.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaXDist.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017C808.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaXIntersect.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017C904.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkLineSegParaXIntersect.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017CB08.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkLineSegParaZDist.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017CEA8.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkPointParaZIntersect.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017CFA4.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriChkLineSegParaZIntersect.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017D1AC.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017D220.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_LineSegVsPlane.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017D404.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_TriSetCoords.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_IsPointInSphere.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_PointDistToLine2D.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017D7C0.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017D814.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017D91C.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017DA24.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_LineVsSph.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017DD34.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColSphereTri.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017E294.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017E350.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColCylinderTri.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017F1A0.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_SphVsSph.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColSphereSphereIntersect.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColSphereSphereIntersectAndDistance.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColSphereCylinderDistance.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColSphereCylinderDistanceAndAmount.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColCylinderCylinderAmount.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_ColCylinderCylinderAmountAndDistance.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3d_ColTriTri.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XZInSphere.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_XYInSphere.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/Math3D_YZInSphere.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017FB1C.s") - -#pragma GLOBAL_ASM("asm/non_matchings/code/sys_math3d/func_8017FD44.s") +#include "prevent_bss_reordering.h" +// clang-format off +// Partial structs taken from "prevent_bss_reordering.h" +struct Dummy200 { int x; }; +struct Dummy201 { int x; }; +struct Dummy202 { int x; }; +struct Dummy203 { int x; }; +struct Dummy204 { int x; }; +struct Dummy205 { int x; }; +struct Dummy206 { int x; }; +struct Dummy207 { int x; }; +struct Dummy208 { int x; }; +struct Dummy209 { int x; }; +struct Dummy210 { int x; }; +struct Dummy211 { int x; }; +struct Dummy212 { int x; }; +// clang-format on + +#include "z64math.h" + +#include "libc/stdbool.h" +#include "PR/gu.h" + +Vec3f gZeroVec3f = { 0.0f, 0.0f, 0.0f }; +Vec3s gZeroVec3s = { 0, 0, 0 }; + +#define ARRAY_COUNT(arr) (s32)(sizeof(arr) / sizeof(arr[0])) + +f32 Math3D_Normalize(Vec3f* vec) { + f32 magnitude = Math3D_Vec3fMagnitude(vec); + + if (IS_ZERO(magnitude)) { + return 0.0f; + } + + vec->x *= 1.0f / magnitude; + vec->y *= 1.0f / magnitude; + vec->z *= 1.0f / magnitude; + return magnitude; +} + +/** + * Creates an infinite line along the intersection of the plane defined from `planeAA`x + `planeAB`y + `planeAB`z + + * `planeADist` = 0 and `planeBA`x + `planeBB`y + `planeBC`z + `planeBDist` = 0, and finds the closest point on that + * intersection to the line segment `linePointA and linePointB`, outputs the intersection to `closestPoint` + */ +s32 Math3D_PlaneVsLineSegClosestPoint(f32 planeAA, f32 planeAB, f32 planeAC, f32 planeADist, f32 planeBA, f32 planeBB, + f32 planeBC, f32 planeBDist, Vec3f* linePointA, Vec3f* linePointB, + Vec3f* closestPoint) { + static InfiniteLine sPlaneIntersectLine; + static Linef sPlaneIntersectSeg; + Vec3f sp34; // unused + + if (!Math3D_PlaneVsPlaneNewLine(planeAA, planeAB, planeAC, planeADist, planeBA, planeBB, planeBC, planeBDist, + &sPlaneIntersectLine)) { + // The planes are parallel + return false; + } + + // create a line segment on the plane. + Math_Vec3f_Copy(&sPlaneIntersectSeg.a, &sPlaneIntersectLine.point); + sPlaneIntersectSeg.b.x = (sPlaneIntersectLine.dir.x * 100.0f) + sPlaneIntersectLine.point.x; + sPlaneIntersectSeg.b.y = (sPlaneIntersectLine.dir.y * 100.0f) + sPlaneIntersectLine.point.y; + sPlaneIntersectSeg.b.z = (sPlaneIntersectLine.dir.z * 100.0f) + sPlaneIntersectLine.point.z; + + // closestPoint is a point on planeIntersect, sp34 is a point on linePointA, linePointB + if (!Math3D_LineSegMakePerpLineSeg(&sPlaneIntersectSeg.a, &sPlaneIntersectSeg.b, linePointA, linePointB, + closestPoint, &sp34)) { + return false; + } + return true; +} + +/** + * Finds the two points on lines A and B where the lines are closest together. + */ +s32 Math3D_LineSegMakePerpLineSeg(Vec3f* lineAPointA, Vec3f* lineAPointB, Vec3f* lineBPointA, Vec3f* lineBPointB, + Vec3f* lineAClosestToB, Vec3f* lineBClosestToA) { + f32 magSq; + f32 scaleB; + f32 lineAx = lineAPointB->x - lineAPointA->x; + f32 lineAy = lineAPointB->y - lineAPointA->y; + f32 lineAz = lineAPointB->z - lineAPointA->z; + f32 lineBx = lineBPointB->x - lineBPointA->x; + f32 lineBy = lineBPointB->y - lineBPointA->y; + f32 lineBz = lineBPointB->z - lineBPointA->z; + f32 compAAlongB; + f32 compBAAlongB; + Vec3f lineAPerpB; + Vec3f lineBAPerpB; + f32 tA; + f32 tB; + + magSq = SQ(lineBx) + SQ(lineBy) + SQ(lineBz); + if (IS_ZERO(magSq)) { + return false; + } + + scaleB = 1.0f / magSq; + + compAAlongB = ((lineAx * lineBx) + (lineAy * lineBy) + (lineAz * lineBz)) * scaleB; + + compBAAlongB = ((lineBx * (lineAPointA->x - lineBPointA->x)) + (lineBy * (lineAPointA->y - lineBPointA->y)) + + (lineBz * (lineAPointA->z - lineBPointA->z))) * + scaleB; + + lineAPerpB.x = lineAx - (lineBx * compAAlongB); + lineAPerpB.y = lineAy - (lineBy * compAAlongB); + lineAPerpB.z = lineAz - (lineBz * compAAlongB); + + magSq = SQXYZ(lineAPerpB); + if (IS_ZERO(magSq)) { + return false; + } + + lineBAPerpB.x = (lineAPointA->x - lineBPointA->x) - (lineBx * compBAAlongB); + lineBAPerpB.y = (lineAPointA->y - lineBPointA->y) - (lineBy * compBAAlongB); + lineBAPerpB.z = (lineAPointA->z - lineBPointA->z) - (lineBz * compBAAlongB); + + tA = -DOTXYZ(lineAPerpB, lineBAPerpB) / magSq; + lineAClosestToB->x = (lineAx * tA) + lineAPointA->x; + lineAClosestToB->y = (lineAy * tA) + lineAPointA->y; + lineAClosestToB->z = (lineAz * tA) + lineAPointA->z; + + tB = (compAAlongB * tA) + compBAAlongB; + lineBClosestToA->x = (lineBx * tB) + lineBPointA->x; + lineBClosestToA->y = (lineBy * tB) + lineBPointA->y; + lineBClosestToA->z = (lineBz * tB) + lineBPointA->z; + + return true; +} + +/** + * Determines the closest point on the line `line` to `pos`, by forming a line perpendicular from + * `point` to `line` closest point is placed in `closestPoint` + */ +f32 Math3D_LineClosestToPoint(InfiniteLine* line, Vec3f* pos, Vec3f* closestPoint) { + f32 dirMagnitudeSq = Math3D_Vec3fMagnitudeSq(&line->dir); + f32 t; + + if (IS_ZERO(dirMagnitudeSq)) { + Math_Vec3f_Copy(closestPoint, pos); + //! @bug Missing early return + } + + t = (((pos->x - line->point.x) * line->dir.x) + ((pos->y - line->point.y) * line->dir.y) + + ((pos->z - line->point.z) * line->dir.z)) / + dirMagnitudeSq; + closestPoint->x = (line->dir.x * t) + line->point.x; + closestPoint->y = (line->dir.y * t) + line->point.y; + closestPoint->z = (line->dir.z * t) + line->point.z; + + return t; +} + +void Math3D_FindPointOnPlaneIntersect(f32 planeAAxis1Norm, f32 planeAAxis2Norm, f32 planeBAxis1Norm, + f32 planeBAxis2Norm, f32 axis3Direction, f32 planeADist, f32 planeBDist, + f32* axis1Point, f32* axis2Point) { + *axis1Point = ((planeAAxis2Norm * planeBDist) - (planeBAxis2Norm * planeADist)) / axis3Direction; + *axis2Point = ((planeBAxis1Norm * planeADist) - (planeAAxis1Norm * planeBDist)) / axis3Direction; +} + +/** + * Creates a line between the intersections of two planes defined from `planeAA`x + `planeAB`y + `planeAC`z + + * `planeADist` = 0 and `planeBA`x + `planeBB`y + `planeBC`z + `planeBDist` = 0, and outputs the line to `intersect`. + * Returns false if the planes are parallel. + */ +s32 Math3D_PlaneVsPlaneNewLine(f32 planeAA, f32 planeAB, f32 planeAC, f32 planeADist, f32 planeBA, f32 planeBB, + f32 planeBC, f32 planeBDist, InfiniteLine* intersect) { + s32 pad; + Vec3f planeANormal; + Vec3f planeBNormal; + f32 dirX; + f32 dirY; + f32 dirZ; + + VEC_SET(planeANormal, planeAA, planeAB, planeAC); + VEC_SET(planeBNormal, planeBA, planeBB, planeBC); + + Math3D_Vec3f_Cross(&planeANormal, &planeBNormal, &intersect->dir); + + if (IS_ZERO(intersect->dir.x) && IS_ZERO(intersect->dir.y) && IS_ZERO(intersect->dir.z)) { + // planes are parallel + return false; + } + + dirX = fabsf(intersect->dir.x); + dirY = fabsf(intersect->dir.y); + dirZ = fabsf(intersect->dir.z); + + if ((dirX >= dirY) && (dirX >= dirZ)) { + Math3D_FindPointOnPlaneIntersect(planeAB, planeAC, planeBB, planeBC, intersect->dir.x, planeADist, planeBDist, + &intersect->point.y, &intersect->point.z); + intersect->point.x = 0.0f; + } else if ((dirY >= dirX) && (dirY >= dirZ)) { + Math3D_FindPointOnPlaneIntersect(planeAC, planeAA, planeBC, planeBA, intersect->dir.y, planeADist, planeBDist, + &intersect->point.z, &intersect->point.x); + intersect->point.y = 0.0f; + } else { + Math3D_FindPointOnPlaneIntersect(planeAA, planeAB, planeBA, planeBB, intersect->dir.z, planeADist, planeBDist, + &intersect->point.x, &intersect->point.y); + intersect->point.z = 0.0f; + } + return true; +} + +/** + * Gets the closest point on the line formed from the intersection of of the planes defined from + * `planeAA`x + `planeAB`y + `planeAC`z + `planeADist` = 0 and + * `planeBA`x + `planeBB`y + `planeBC`z + `planeBDist` = 0 + * the point on the intersection line closest to `point` is placed in `closestPoint` + * returns false if the planes are parallel. + */ +s32 Math3D_PlaneVsPlaneVsLineClosestPoint(f32 planeAA, f32 planeAB, f32 planeAC, f32 planeADist, f32 planeBA, + f32 planeBB, f32 planeBC, f32 planeBDist, Vec3f* point, Vec3f* closestPoint) { + static InfiniteLine sPlaneIntersect; + + if (!Math3D_PlaneVsPlaneNewLine(planeAA, planeAB, planeAC, planeADist, planeBA, planeBB, planeBC, planeBDist, + &sPlaneIntersect)) { + return false; + } + Math3D_LineClosestToPoint(&sPlaneIntersect, point, closestPoint); + return true; +} + +/** + * Calculates the point on the line from starting point `v0`, in the direction `dir` scaled by `scale`. Result is placed + * in `ret` + */ +void Math3D_PointOnDirectedLine(Vec3f* v0, Vec3f* dir, f32 scale, Vec3f* ret) { + ret->x = (dir->x * scale) + v0->x; + ret->y = (dir->y * scale) + v0->y; + ret->z = (dir->z * scale) + v0->z; +} + +/** + * Splits the line segment from end points `v0` and `v1`, and splits that segment + * by `ratio` of `v0`:`v1`, places the resulting point on the line in `ret` + */ +void Math3D_LineSplitRatio(Vec3f* v0, Vec3f* v1, f32 ratio, Vec3f* ret) { + Vec3f diff; + + Math_Vec3f_Diff(v1, v0, &diff); + Math3D_PointOnDirectedLine(v0, &diff, ratio, ret); +} + +/** + * Calculates the cosine between vectors `a` and `b` + */ +f32 Math3D_Cos(Vec3f* a, Vec3f* b) { + f32 ret; + + Math3D_CosOut(a, b, &ret); + return ret; +} + +/** + * Calculates the cosine between vectors `a` and `b` and places the result in `dst` + * returns true if the cosine cannot be calculated because the product of the magnitudes is zero + */ +s32 Math3D_CosOut(Vec3f* a, Vec3f* b, f32* dst) { + f32 magProduct = Math3D_Vec3fMagnitude(a) * Math3D_Vec3fMagnitude(b); + + if (IS_ZERO(magProduct)) { + *dst = 0.0f; + return true; + } + *dst = ((a->x * b->x) + (a->y * b->y) + (a->z * b->z)) / magProduct; + return false; +} + +/** + * Reflects vector `vec` across the normal vector `normal`, reflection vector is placed in + * `reflVec` + */ +void Math3D_Vec3fReflect(Vec3f* vec, Vec3f* normal, Vec3f* reflVec) { + f32 normScaleY; + Vec3f negVec; + f32 normScaleZ; + f32 normScaleX; + f32 vecDotNorm; + + negVec.x = vec->x * -1.0f; + negVec.y = vec->y * -1.0f; + negVec.z = vec->z * -1.0f; + + vecDotNorm = Math3D_Cos(&negVec, normal); + + normScaleX = normal->x * vecDotNorm; + normScaleY = normal->y * vecDotNorm; + normScaleZ = normal->z * vecDotNorm; + + reflVec->x = ((normScaleX + vec->x) + (normScaleX + vec->x)) + negVec.x; + reflVec->y = ((normScaleY + vec->y) + (normScaleY + vec->y)) + negVec.y; + reflVec->z = ((normScaleZ + vec->z) + (normScaleZ + vec->z)) + negVec.z; +} + +/** + * Checks if the point (`x`,`y`) is contained within the square formed from (`upperLeftX`,`upperLeftY`) to + * (`lowerRightX`,`lowerRightY`) + */ +s32 Math3D_PointInSquare2D(f32 upperLeftX, f32 lowerRightX, f32 upperLeftY, f32 lowerRightY, f32 x, f32 y) { + if ((x >= upperLeftX) && (x <= lowerRightX) && (y >= upperLeftY) && (y <= lowerRightY)) { + return true; + } + return false; +} + +/** + * Checks if the square in the XY planed formed around the circle with center (`centerX`,`centerY`) + * with radius `radius` touches any portion of the square formed around the triangle formed from `v0`, `v1`, and `v2` + */ +s32 Math3D_CirSquareVsTriSquareXY(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 centerX, f32 centerY, f32 radius) { + f32 min; + f32 max; + + if (v0->x < v1->x) { + min = v0->x; + max = v1->x; + } else { + min = v1->x; + max = v0->x; + } + + if (min > v2->x) { + min = v2->x; + } else if (max < v2->x) { + max = v2->x; + } + + if ((centerX < (min - radius)) || ((max + radius) < centerX)) { + return false; + } + if (v0->y < v1->y) { + min = v0->y; + max = v1->y; + } else { + min = v1->y; + max = v0->y; + } + if (min > v2->y) { + min = v2->y; + } else if (max < v2->y) { + max = v2->y; + } + + if ((centerY < (min - radius)) || (centerY > (max + radius))) { + return false; + } + return true; +} + +/** + * Checks if the square in the YZ planed formed around the circle with center (`centerY`,`centerZ`) + * with radius `radius` touches any portion of the square formed around the triangle formed from `v0`, `v1`, and `v2` + */ +s32 Math3D_CirSquareVsTriSquareYZ(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 centerY, f32 centerZ, f32 radius) { + f32 min; + f32 max; + + if (v0->z < v1->z) { + min = v0->z; + max = v1->z; + } else { + min = v1->z; + max = v0->z; + } + + if (min > v2->z) { + min = v2->z; + } else if (max < v2->z) { + max = v2->z; + } + + if ((centerZ < (min - radius)) || ((max + radius) < centerZ)) { + return false; + } + + if (v0->y < v1->y) { + min = v0->y; + max = v1->y; + } else { + min = v1->y; + max = v0->y; + } + + if (min > v2->y) { + min = v2->y; + } else if (max < v2->y) { + max = v2->y; + } + + if ((centerY < (min - radius)) || ((max + radius) < centerY)) { + return false; + } + return true; +} + +/** + * Checks if the square in the ZX planed formed around the circle with center (`centerZ`,`centerX`) + * with radius `radius` touches any portion of the square formed around the triangle formed from `v0`, `v1`, and `v2` + */ +s32 Math3D_CirSquareVsTriSquareZX(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 centerZ, f32 centerX, f32 radius) { + f32 min; + f32 max; + + if (v0->x < v1->x) { + min = v0->x; + max = v1->x; + } else { + min = v1->x; + max = v0->x; + } + + if (min > v2->x) { + min = v2->x; + } else if (max < v2->x) { + max = v2->x; + } + + if ((centerX < (min - radius)) || ((max + radius) < centerX)) { + return false; + } + + if (v0->z < v1->z) { + min = v0->z; + max = v1->z; + } else { + min = v1->z; + max = v0->z; + } + + if (min > v2->z) { + min = v2->z; + } else if (max < v2->z) { + max = v2->z; + } + + if ((centerZ < (min - radius)) || ((max + radius) < centerZ)) { + return false; + } + return true; +} + +/** + * Checks if the cube formed around the triangle formed from `v0`, `v1`, and `v2` + * has any portion touching the cube formed around the sphere with center `center` + * and radius of `radius` + */ +s32 Math3D_SphCubeVsTriCube(Vec3f* v0, Vec3f* v1, Vec3f* v2, Vec3f* center, f32 radius) { + f32 min; + f32 max; + + if (v0->x < v1->x) { + min = v0->x; + max = v1->x; + } else { + min = v1->x; + max = v0->x; + } + + if (min > v2->x) { + min = v2->x; + } else if (max < v2->x) { + max = v2->x; + } + + if ((center->x < (min - radius)) || ((max + radius) < center->x)) { + return false; + } + + if (v0->z < v1->z) { + min = v0->z; + max = v1->z; + } else { + min = v1->z; + max = v0->z; + } + + if (min > v2->z) { + min = v2->z; + } else if (max < v2->z) { + max = v2->z; + } + + if ((center->z < (min - radius)) || ((max + radius) < center->z)) { + return false; + } + + if (v0->y < v1->y) { + min = v0->y; + max = v1->y; + } else { + min = v1->y; + max = v0->y; + } + + if (min > v2->y) { + min = v2->y; + } else if (max < v2->y) { + max = v2->y; + } + + if ((center->y < (min - radius)) || ((max + radius) < center->y)) { + return false; + } + return true; +} + +/** + * Returns the distance squared between `a` and `b` on a single axis + */ +f32 Math3D_Dist1DSq(f32 a, f32 b) { + return SQ(a) + SQ(b); +} + +/** + * Returns the distance between `a` and `b` on a single axis + */ +f32 Math3D_Dist1D(f32 a, f32 b) { + return sqrtf(Math3D_Dist1DSq(a, b)); +} + +/** + * Returns the distance squared between (`x0`,`y0`) and (`x1`,`x2`) + */ +f32 Math3D_Dist2DSq(f32 x0, f32 y0, f32 x1, f32 y1) { + return Math3D_Dist1DSq(x0 - x1, y0 - y1); +} + +/** + * Returns the distance between points (`x0`,`y0`) and (`x1`,`y1`) + */ +f32 Math3D_Dist2D(f32 x0, f32 y0, f32 x1, f32 y1) { + return sqrtf(Math3D_Dist2DSq(x0, y0, x1, y1)); +} + +/** + * Returns the magnitude (length) squared of `vec` + */ +f32 Math3D_Vec3fMagnitudeSq(Vec3f* vec) { + return SQ(vec->x) + SQ(vec->y) + SQ(vec->z); +} + +/** + * Returns the magnitude (length) of `vec` + */ +f32 Math3D_Vec3fMagnitude(Vec3f* vec) { + return sqrtf(Math3D_Vec3fMagnitudeSq(vec)); +} + +/** + * Returns the distance between `a` and `b` squared. + */ +f32 Math3D_Vec3fDistSq(Vec3f* a, Vec3f* b) { + Vec3f diff; + + Math_Vec3f_Diff(a, b, &diff); + + return Math3D_Vec3fMagnitudeSq(&diff); +} + +/* + * Calculates the distance between points `a` and `b` + */ +f32 Math3D_Vec3f_DistXYZ(Vec3f* a, Vec3f* b) { + return Math_Vec3f_DistXYZ(a, b); +} + +/* + * Calculates the distance between `a` and `b`. + */ +f32 Math3D_DistXYZ16toF(Vec3s* a, Vec3f* b) { + Vec3f diff; + + diff.x = a->x - b->x; + diff.y = a->y - b->y; + diff.z = a->z - b->z; + + return Math3D_Vec3fMagnitude(&diff); +} + +static Vec3f sABDiff; +static Vec3f sACDiff; + +/** + * Gets the Z portion of the cross product of vectors `a - (`dx`,`dy`,z) and `b` - (`dx`,`dy`,z) + */ +f32 Math3D_Vec3fDiff_CrossZ(Vec3f* a, Vec3f* b, f32 dx, f32 dy) { + return ((a->x - dx) * (b->y - dy)) - ((a->y - dy) * (b->x - dx)); +} + +/** + * Gets the X portion of the cross product of vectors `a - (x,`dy`,`dz`) and `b` - (x,`dy`,`dz`) + */ +f32 Math3D_Vec3fDiff_CrossX(Vec3f* a, Vec3f* b, f32 dy, f32 dz) { + return ((a->y - dy) * (b->z - dz)) - ((a->z - dz) * (b->y - dy)); +} + +/** + * Gets the Y portion of the cross product of vectors `a - (`dx`,y,`dz`) and `b` - (`dx`,y,`dz`) + */ +f32 Math3D_Vec3fDiff_CrossY(Vec3f* a, Vec3f* b, f32 dz, f32 dx) { + return ((a->z - dz) * (b->x - dx)) - ((a->x - dx) * (b->z - dz)); +} + +/** + * Gets the Cross Product of vectors `a` and `b` and places the result in `ret` + */ +void Math3D_Vec3f_Cross(Vec3f* a, Vec3f* b, Vec3f* ret) { + ret->x = (a->y * b->z) - (a->z * b->y); + ret->y = (a->z * b->x) - (a->x * b->z); + ret->z = (a->x * b->y) - (a->y * b->x); +} + +/* + * Calculates the normal vector to a surface with sides `vb` - `va` and `vc` - `va` + * outputs the normal to `normal` + */ +void Math3D_SurfaceNorm(Vec3f* va, Vec3f* vb, Vec3f* vc, Vec3f* normal) { + Math_Vec3f_Diff(vb, va, &sABDiff); + Math_Vec3f_Diff(vc, va, &sACDiff); + Math3D_Vec3f_Cross(&sABDiff, &sACDiff, normal); +} + +/** + * Creates flags relative to the faces of a cube. + */ +s32 Math3D_PointRelativeToCubeFaces(Vec3f* point, Vec3f* min, Vec3f* max) { + s32 ret = 0; + + if (point->x > max->x) { + ret = 1; + } else if (point->x < min->x) { + ret |= 2; + } + + if (point->y > max->y) { + ret |= 4; + } else if (point->y < min->y) { + ret |= 8; + } + + if (point->z > max->z) { + ret |= 0x10; + } else if (point->z < min->z) { + ret |= 0x20; + } + + return ret; +} + +/** + * Creates flags of `point` relative to the edges of a cube + */ +s32 Math3D_PointRelativeToCubeEdges(Vec3f* point, Vec3f* min, Vec3f* max) { + s32 ret = 0; + + if ((-min->x + max->y) < (-point->x + point->y)) { + ret |= 1; + } + + if ((-point->x + point->y) < (-max->x + min->y)) { + ret |= 2; + } + + if ((max->x + max->y) < (point->x + point->y)) { + ret |= 4; + } + + if ((point->x + point->y) < (min->x + min->y)) { + ret |= 8; + } + + if ((-min->z + max->y) < (-point->z + point->y)) { + ret |= 0x10; + } + + if ((-point->z + point->y) < (-max->z + min->y)) { + ret |= 0x20; + } + + if ((max->z + max->y) < (point->z + point->y)) { + ret |= 0x40; + } + + if ((point->z + point->y) < (min->z + min->y)) { + ret |= 0x80; + } + + if ((-min->z + max->x) < (-point->z + point->x)) { + ret |= 0x100; + } + + if ((-point->z + point->x) < (-max->z + min->x)) { + ret |= 0x200; + } + + if ((max->z + max->x) < (point->z + point->x)) { + ret |= 0x400; + } + + if ((point->z + point->x) < (min->z + min->x)) { + ret |= 0x800; + } + return ret; +} + +/** + * Creates flags for `point` relative to the vertices of a cube + */ +s32 Math3D_PointRelativeToCubeVertices(Vec3f* point, Vec3f* min, Vec3f* max) { + s32 ret = 0; + + if ((max->x + max->y + max->z) < (point->x + point->y + point->z)) { + ret = 1; + } + + if ((-min->x + max->y + max->z) < (-point->x + point->y + point->z)) { + ret |= 2; + } + + if ((-min->x + max->y - min->z) < (-point->x + point->y - point->z)) { + ret |= 4; + } + + if ((max->x + max->y - min->z) < (point->x + point->y - point->z)) { + ret |= 8; + } + + if ((max->x - min->y + max->z) < (point->x - point->y + point->z)) { + ret |= 0x10; + } + + //! @bug: The next 2 conditions are the same check. + if ((-min->x - min->y + max->z) < (-point->x - point->y + point->z)) { + ret |= 0x20; + } + + if ((-min->x - min->y + max->z) < (-point->x - point->y + point->z)) { + ret |= 0x40; + } + + if ((-min->x - min->y - min->z) < (-point->x - point->y - point->z)) { + ret |= 0x80; + } + return ret; +} + +/** + * Checks if a line segment with endpoints `a` and `b` intersect a cube + */ +s32 Math3D_LineVsCube(Vec3f* min, Vec3f* max, Vec3f* a, Vec3f* b) { + static Vec3f sTriVtx0; + static Vec3f sTriVtx1; + static Vec3f sTriVtx2; + static Vec3f sIntersectPoint; + s32 flags[2]; + + flags[0] = flags[1] = 0; + flags[0] = Math3D_PointRelativeToCubeFaces(a, min, max); + if (!flags[0]) { + return true; + } + + flags[1] = Math3D_PointRelativeToCubeFaces(b, min, max); + if (!flags[1]) { + return true; + } + + if (flags[0] & flags[1]) { + return false; + } + + flags[0] |= (Math3D_PointRelativeToCubeEdges(a, min, max) << 8); + flags[1] |= (Math3D_PointRelativeToCubeEdges(b, min, max) << 8); + if (flags[0] & flags[1]) { + return false; + } + + flags[0] |= (Math3D_PointRelativeToCubeVertices(a, min, max) << 0x18); + flags[1] |= (Math3D_PointRelativeToCubeVertices(b, min, max) << 0x18); + if (flags[0] & flags[1]) { + return false; + } + + // face 1 + sTriVtx0.x = min->x; + sTriVtx0.y = min->y; + sTriVtx0.z = min->z; + sTriVtx1.x = min->x; + sTriVtx1.y = min->y; + sTriVtx1.z = max->z; + sTriVtx2.x = min->x; + sTriVtx2.y = max->y; + sTriVtx2.z = max->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, -1.0f, 0.0f, 0.0f, min->x, a, b, &sIntersectPoint, + 0)) { + return true; + } + + sTriVtx1.x = min->x; + sTriVtx1.y = max->y; + sTriVtx1.z = max->z; + sTriVtx2.x = min->x; + sTriVtx2.y = max->y; + sTriVtx2.z = min->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, -1.0f, 0.0f, 0.0f, min->x, a, b, &sIntersectPoint, + 0)) { + return true; + } + + // face 2 + sTriVtx0.x = min->x; + sTriVtx0.y = max->y; + sTriVtx0.z = max->z; + sTriVtx1.x = min->x; + sTriVtx1.y = min->y; + sTriVtx1.z = max->z; + sTriVtx2.x = max->x; + sTriVtx2.y = max->y; + sTriVtx2.z = max->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, 1.0f, -max->z, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx0.x = max->x; + sTriVtx0.y = max->y; + sTriVtx0.z = max->z; + sTriVtx2.x = max->x; + //! @bug trVtx1.y should be sTriVtx2.y, prevents a tri on the cube from being checked. + sTriVtx1.y = min->y; + sTriVtx2.z = max->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, 1.0f, -max->z, a, b, &sIntersectPoint, + 0)) { + return true; + } + + // face 3 + sTriVtx1.x = min->x; + sTriVtx1.y = max->y; + sTriVtx1.z = min->z; + sTriVtx2.x = min->x; + sTriVtx2.y = max->y; + sTriVtx2.z = max->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 1.0f, 0.0f, -max->y, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx1.x = max->x; + sTriVtx1.y = max->y; + sTriVtx1.z = min->z; + sTriVtx2.x = min->x; + sTriVtx2.y = max->y; + sTriVtx2.z = min->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 1.0f, 0.0f, -max->y, a, b, &sIntersectPoint, + 0)) { + return true; + } + + // face 4 + sTriVtx0.x = min->x; + sTriVtx0.y = min->y; + sTriVtx0.z = min->z; + sTriVtx1.x = min->x; + sTriVtx1.y = max->y; + sTriVtx1.z = min->z; + sTriVtx2.x = max->x; + sTriVtx2.y = max->y; + sTriVtx2.z = min->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, -1.0f, min->z, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx1.x = max->x; + sTriVtx1.y = max->y; + sTriVtx1.z = min->z; + sTriVtx2.x = max->x; + sTriVtx2.y = min->y; + sTriVtx2.z = min->z; + + // face 5 + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, -1.0f, min->z, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx1.x = max->x; + sTriVtx1.y = min->y; + sTriVtx1.z = min->z; + sTriVtx2.x = max->x; + sTriVtx2.y = min->y; + sTriVtx2.z = max->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, -1.0f, 0.0f, min->y, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx1.x = max->x; + sTriVtx1.y = min->y; + sTriVtx1.z = max->z; + sTriVtx2.x = min->x; + sTriVtx2.y = min->y; + sTriVtx2.z = max->z; + + // face 6 + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, -1.0f, 0.0f, min->y, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx0.x = max->x; + sTriVtx0.y = max->y; + sTriVtx0.z = max->z; + sTriVtx1.x = max->x; + sTriVtx1.y = min->y; + sTriVtx1.z = min->z; + sTriVtx2.x = max->x; + sTriVtx2.y = max->y; + sTriVtx2.z = min->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 1.0f, 0.0f, 0.0f, -max->x, a, b, &sIntersectPoint, + 0)) { + return true; + } + sTriVtx1.x = max->x; + sTriVtx1.y = min->y; + sTriVtx1.z = max->z; + sTriVtx2.x = max->x; + sTriVtx2.y = min->y; + sTriVtx2.z = min->z; + if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 1.0f, 0.0f, 0.0f, -max->x, a, b, &sIntersectPoint, + 0)) { + return true; + } + + return false; +} + +/** + * Checks if a line segment with endpoints `a` and `b` intersect a cube + */ +s32 Math3D_LineVsCubeShort(Vec3s* min, Vec3s* max, Vec3s* a, Vec3s* b) { + static Vec3f sMinF; + static Vec3f sMaxF; + static Vec3f sAF; + static Vec3f sBF; + + sMinF.x = min->x; + sMinF.y = min->y; + sMinF.z = min->z; + sMaxF.x = max->x; + sMaxF.y = max->y; + sMaxF.z = max->z; + sAF.x = a->x; + sAF.y = a->y; + sAF.z = a->z; + sBF.x = b->x; + sBF.y = b->y; + sBF.z = b->z; + + return Math3D_LineVsCube(&sMinF, &sMaxF, &sAF, &sBF); +} + +/** + * Rotates the xz plane around the y axis `angle` degrees. + * outputs the plane equation `a``pointOnPlane->x` + 0y + `c``pointOnPlane->z`+`d` = 0 + */ +void Math3D_RotateXZPlane(Vec3f* pointOnPlane, s16 angle, f32* a, f32* c, f32* d) { + *a = Math_SinS(angle) * 0x7FFF; + *c = Math_CosS(angle) * 0x7FFF; + *d = -((*a * pointOnPlane->x) + (*c * pointOnPlane->z)); +} + +/* + * Defines a plane from vertices `va`, `vb`, and `vc`. Normal components are output to + * `nx`, `ny`, and `nz`. Distance from the origin is output to `originDist` + * Satisfies the plane equation NxVx + NyVy + NzVz + D = 0 + */ +void Math3D_DefPlane(Vec3f* va, Vec3f* vb, Vec3f* vc, f32* nx, f32* ny, f32* nz, f32* originDist) { + static Vec3f sNormal; + f32 normMagnitude; + f32 normMagInv; + + Math3D_SurfaceNorm(va, vb, vc, &sNormal); + normMagnitude = sqrtf(SQ(sNormal.x) + SQ(sNormal.y) + SQ(sNormal.z)); + if (!IS_ZERO(normMagnitude)) { + normMagInv = 1.0f / normMagnitude; + *nx = sNormal.x * normMagInv; + *ny = sNormal.y * normMagInv; + *nz = sNormal.z * normMagInv; + *originDist = -((*nx * va->x) + (*ny * va->y) + (*nz * va->z)); + } else { + *originDist = 0.0f; + *nz = 0.0f; + *ny = 0.0f; + *nx = 0.0f; + } +} + +/* + * Returns the answer to the plane equation with elements specified by arguments. + */ +f32 Math3D_PlaneF(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* pointOnPlane) { + return (nx * pointOnPlane->x) + (ny * pointOnPlane->y) + (nz * pointOnPlane->z) + originDist; +} + +/* + * Returns the answer to the plane equation + */ +f32 Math3D_Plane(Plane* plane, Vec3f* pointOnPlane) { + return (plane->normal.x * pointOnPlane->x) + (plane->normal.y * pointOnPlane->y) + + (plane->normal.z * pointOnPlane->z) + plane->originDist; +} + +/* + * Calculates the absolute distance from a point `p` to the plane defined as + * `nx`, `ny`, `nz`, and `originDist` + */ +f32 Math3D_UDistPlaneToPos(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* p) { + return fabsf(Math3D_DistPlaneToPos(nx, ny, nz, originDist, p)); +} + +/* + * Calculates the signed distance from a point `p` to a plane defined as + * `nx`, `ny`, `nz`, and `originDist` + */ +f32 Math3D_DistPlaneToPos(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* p) { + f32 normMagnitude = sqrtf(SQ(nx) + SQ(ny) + SQ(nz)); + + if (IS_ZERO(normMagnitude)) { + return 0.0f; + } + return Math3D_PlaneF(nx, ny, nz, originDist, p) / normMagnitude; +} + +/** + * Checks if the point defined by (`z`,`x`) is within distance of the triangle defined from `v0`,`v1`, and `v2` + */ +s32 Math3D_TriChkPointParaYImpl(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x, f32 detMax, f32 chkDist, f32 ny) { + f32 detv0v1; + f32 detv1v2; + f32 detv2v0; + f32 distToEdgeSq; + f32 chkDistSq; + + // first check if the point is within range of the triangle. + if (!Math3D_CirSquareVsTriSquareZX(v0, v1, v2, z, x, chkDist)) { + return false; + } + + // check if the point is within `chkDist` units of any vertex of the triangle. + chkDistSq = SQ(chkDist); + if (((SQ(v0->z - z) + SQ(v0->x - x)) < chkDistSq) || ((SQ(v1->z - z) + SQ(v1->x - x)) < chkDistSq) || + ((SQ(v2->z - z) + SQ(v2->x - x)) < chkDistSq)) { + return true; + } + + // Calculate the determinant of each face of the triangle to the point. + // If all the of determinants are within abs(`detMax`), return true. + if (((detMax >= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) && + (detMax >= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) && + (detMax >= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) { + return true; + } + + if (((-detMax <= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) && + (-detMax <= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) && + (-detMax <= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) { + return true; + } + + if ((fabsf(ny) > 0.5f) && (chkDistSq > 0.0f)) { + // Do a check on each face of the triangle, if the point is within `chkDist` units return true. + if (Math3D_PointDistSqToLineZX(z, x, v0, v1, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + if (Math3D_PointDistSqToLineZX(z, x, v1, v2, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + if (Math3D_PointDistSqToLineZX(z, x, v2, v0, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + } + return false; +} + +s32 Math3D_TriChkPointParaYDeterminate(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x, f32 detMax, f32 ny) { + return Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, detMax, 1.0f, ny); +} + +s32 Math3D_TriChkPointParaYSlopedY(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x) { + return Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, 1.0f, 0.6f); +} + +/** + * Performs the triangle and point check parallel to the Y axis, outputs the y coordinate of the point to `yIntersect` + */ +s32 Math3D_TriChkPointParaYIntersectDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 z, + f32 x, f32* yIntersect, f32 chkDist) { + if (IS_ZERO(ny)) { + return false; + } + + if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, chkDist, ny)) { + *yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny; + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaYIntersectInsideTri(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, + f32 z, f32 x, f32* yIntersect, f32 chkDist) { + if (IS_ZERO(ny)) { + return false; + } + + if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 0.0f, chkDist, ny)) { + *yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny; + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaY(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 ny, f32 z, f32 x) { + if (IS_ZERO(ny)) { + return false; + } + + if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, 1.0f, ny)) { + return true; + } + + return false; +} + +s32 Math3D_TriChkLineSegParaYIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 z, + f32 x, f32* yIntersect, f32 y0, f32 y1) { + f32 pointADist; + f32 pointBDist; + Vec3f planePos; + + if (IS_ZERO(ny)) { + return false; + } + + planePos.x = x; + planePos.y = y0; + planePos.z = z; + + pointADist = Math3D_PlaneF(nx, ny, nz, originDist, &planePos); + planePos.y = y1; + pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, &planePos); + + if (((pointADist > 0.0f) && (pointBDist > 0.0f)) || ((pointADist < 0.0f) && (pointBDist < 0.0f))) { + return false; + } + + if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, 1.0f, ny)) { + *yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny; + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaYDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, Plane* plane, f32 z, f32 x, f32 chkDist) { + if (IS_ZERO(plane->normal.y)) { + return false; + } + + if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 0.0f, chkDist, plane->normal.y)) { + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaYImplNoCheckRange(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x, f32 detMax, f32 chkDist, + f32 ny) { + f32 detv0v1; + f32 detv1v2; + f32 detv2v0; + f32 distToEdgeSq; + f32 chkDistSq; + + // check if the point is within `chkDist` units of any vertex of the triangle. + chkDistSq = SQ(chkDist); + if (((SQ(v0->z - z) + SQ(v0->x - x)) < chkDistSq) || ((SQ(v1->z - z) + SQ(v1->x - x)) < chkDistSq) || + ((SQ(v2->z - z) + SQ(v2->x - x)) < chkDistSq)) { + return true; + } + + // Calculate the determinant of each face of the triangle to the point. + // If all the of determinants are within abs(`detMax`), return true. + if (((detMax >= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) && + (detMax >= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) && + (detMax >= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) { + return true; + } + if (((-detMax <= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) && + (-detMax <= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) && + (-detMax <= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) { + return true; + } + + if ((fabsf(ny) > 0.5f) && (chkDistSq > 0.0f)) { + // Do a check on each face of the triangle, if the point is within `chkDist` units return true. + if (Math3D_PointDistSqToLineZX(z, x, v0, v1, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + if (Math3D_PointDistSqToLineZX(z, x, v1, v2, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + if (Math3D_PointDistSqToLineZX(z, x, v2, v0, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + } + + return false; +} + +s32 Math3D_TriChkPointParaYNoRangeCheckIntersectInsideTri(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, + f32 originDist, f32 z, f32 x, f32* yIntersect, f32 chkDist) { + if (IS_ZERO(ny)) { + return false; + } + + if (Math3D_TriChkPointParaYImplNoCheckRange(v0, v1, v2, z, x, 0.0f, chkDist, ny)) { + *yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny; + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaXImpl(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 y, f32 z, f32 detMax, f32 chkDist, f32 ny) { + f32 detv0v1; + f32 detv1v2; + f32 detv2v0; + f32 distToEdgeSq; + f32 chkDistSq; + + // first check if the point is within range of the triangle. + if (!Math3D_CirSquareVsTriSquareYZ(v0, v1, v2, y, z, chkDist)) { + return false; + } + + // check if the point is within `chkDist` units of any vertex of the triangle. + chkDistSq = SQ(chkDist); + if (((SQ(v0->y - y) + SQ(v0->z - z)) < chkDistSq) || ((SQ(v1->y - y) + SQ(v1->z - z)) < chkDistSq) || + ((SQ(v2->y - y) + SQ(v2->z - z)) < chkDistSq)) { + return true; + } + + // Calculate the determinant of each face of the triangle to the point. + // If all the of determinants are within abs(`detMax`), return true. + if (((detMax >= (detv0v1 = ((v0->y - y) * (v1->z - z)) - ((v0->z - z) * (v1->y - y)))) && + (detMax >= (detv1v2 = ((v1->y - y) * (v2->z - z)) - ((v1->z - z) * (v2->y - y)))) && + (detMax >= (detv2v0 = ((v2->y - y) * (v0->z - z)) - ((v2->z - z) * (v0->y - y)))))) { + return true; + } + if (((-detMax <= (detv0v1 = ((v0->y - y) * (v1->z - z)) - ((v0->z - z) * (v1->y - y)))) && + (-detMax <= (detv1v2 = ((v1->y - y) * (v2->z - z)) - ((v1->z - z) * (v2->y - y)))) && + (-detMax <= (detv2v0 = ((v2->y - y) * (v0->z - z)) - ((v2->z - z) * (v0->y - y)))))) { + return true; + } + + if ((fabsf(ny) > 0.5f) && (chkDistSq > 0.0f)) { + // Do a check on each face of the triangle, if the point is within `chkDist` units return true. + if ((Math3D_PointDistSqToLineYZ(y, z, v0, v1, &distToEdgeSq) != 0) && (distToEdgeSq < chkDistSq)) { + return true; + } + if ((Math3D_PointDistSqToLineYZ(y, z, v1, v2, &distToEdgeSq) != 0) && (distToEdgeSq < chkDistSq)) { + return true; + } + if ((Math3D_PointDistSqToLineYZ(y, z, v2, v0, &distToEdgeSq) != 0) && (distToEdgeSq < chkDistSq)) { + return true; + } + } + return false; +} + +s32 Math3D_TriChkPointParaXDeterminate(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 y, f32 z, f32 detMax, f32 nx) { + return Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, detMax, 1.0f, nx); +} + +s32 Math3D_TriChkPointParaXIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 y, + f32 z, f32* xIntersect) { + if (IS_ZERO(nx)) { + return false; + } + + if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) { + *xIntersect = (((-ny * y) - (nz * z)) - originDist) / nx; + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaX(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 y, f32 z) { + if (IS_ZERO(nx)) { + return false; + } + + if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) { + return true; + } + + return false; +} + +s32 Math3D_TriChkLineSegParaXIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 y, + f32 z, f32* xIntersect, f32 x0, f32 x1) { + static Vec3f sPlanePos; + f32 pointADist; + f32 pointBDist; + + if (IS_ZERO(nx)) { + return false; + } + + sPlanePos.x = x0; + sPlanePos.y = y; + sPlanePos.z = z; + pointADist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos); + + sPlanePos.x = x1; + pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos); + + if (((pointADist > 0.0f) && (pointBDist > 0.0f)) || ((pointADist < 0.0f) && (pointBDist < 0.0f))) { + return false; + } + + if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) { + *xIntersect = (((-ny * y) - (nz * z)) - originDist) / nx; + return true; + } + return false; +} + +s32 Math3D_TriChkLineSegParaXDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, Plane* plane, f32 y, f32 z, f32 chkDist) { + if (IS_ZERO(plane->normal.x)) { + return false; + } + + if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 0.0f, chkDist, plane->normal.x)) { + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaZImpl(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 x, f32 y, f32 detMax, f32 chkDist, f32 nz) { + f32 detv0v1; + f32 detv1v2; + f32 detv2v0; + f32 distToEdgeSq; + f32 chkDistSq; + + if (!Math3D_CirSquareVsTriSquareXY(v0, v1, v2, x, y, chkDist)) { + return false; + } + + chkDistSq = SQ(chkDist); + + if (((SQ(x - v0->x) + SQ(y - v0->y)) < chkDistSq) || ((SQ(x - v1->x) + SQ(y - v1->y)) < chkDistSq) || + ((SQ(x - v2->x) + SQ(y - v2->y)) < chkDistSq)) { + // Distance from any vertex to a point is less than chkDist + return true; + } + + if (((detMax >= (detv0v1 = ((v0->x - x) * (v1->y - y)) - ((v0->y - y) * (v1->x - x)))) && + (detMax >= (detv1v2 = ((v1->x - x) * (v2->y - y)) - ((v1->y - y) * (v2->x - x)))) && + (detMax >= (detv2v0 = ((v2->x - x) * (v0->y - y)) - ((v2->y - y) * (v0->x - x)))))) { + return true; + } + + if (((-detMax <= (detv0v1 = ((v0->x - x) * (v1->y - y)) - ((v0->y - y) * (v1->x - x)))) && + (-detMax <= (detv1v2 = ((v1->x - x) * (v2->y - y)) - ((v1->y - y) * (v2->x - x)))) && + (-detMax <= (detv2v0 = ((v2->x - x) * (v0->y - y)) - ((v2->y - y) * (v0->x - x)))))) { + return true; + } + + if (fabsf(nz) > 0.5f && chkDistSq > 0.0f) { + + if (Math3D_PointDistSqToLineXY(x, y, v0, v1, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + + if (Math3D_PointDistSqToLineXY(x, y, v1, v2, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + + if (Math3D_PointDistSqToLineXY(x, y, v2, v0, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) { + return true; + } + } + + return false; +} + +s32 Math3D_TriChkPointParaZDeterminate(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 y, f32 z, f32 detMax, f32 nx) { + return Math3D_TriChkPointParaZImpl(v0, v1, v2, y, z, detMax, 1.0f, nx); +} + +s32 Math3D_TriChkPointParaZIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 x, + f32 y, f32* zIntersect) { + if (IS_ZERO(nz)) { + return false; + } + + if (Math3D_TriChkPointParaZImpl(v0, v1, v2, x, y, 300.0f, 1.0f, nz)) { + *zIntersect = (((-nx * x) - (ny * y)) - originDist) / nz; + return true; + } + + return false; +} + +s32 Math3D_TriChkPointParaZ(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 y, f32 z) { + if (IS_ZERO(nx)) { + return false; + } + + if (Math3D_TriChkPointParaZImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) { + return true; + } + + return false; +} + +s32 Math3D_TriChkLineSegParaZIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 x, + f32 y, f32* zIntersect, f32 z0, f32 z1) { + static Vec3f sPlanePos; + f32 pointADist; + f32 pointBDist; + + if (IS_ZERO(nz)) { + return false; + } + + sPlanePos.x = x; + sPlanePos.y = y; + sPlanePos.z = z0; + pointADist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos); + + sPlanePos.z = z1; + pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos); + + if (((pointADist > 0.0f) && (pointBDist > 0.0f)) || ((pointADist < 0.0f) && (pointBDist < 0.0f))) { + // points on the line segment are on the same side of the plane + return false; + } + + if (Math3D_TriChkPointParaZImpl(v0, v1, v2, x, y, 300.0f, 1.0f, nz)) { + *zIntersect = (((-nx * x) - (ny * y)) - originDist) / nz; + return true; + } + return false; +} + +s32 Math3D_TriChkLineSegParaZDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, Plane* plane, f32 x, f32 y, f32 chkDist) { + if (IS_ZERO(plane->normal.z)) { + return false; + } + + if (Math3D_TriChkPointParaZImpl(v0, v1, v2, x, y, 0.0f, chkDist, plane->normal.z)) { + return true; + } + + return false; +} + +s32 Math3D_LineSegFindPlaneIntersect(f32 pointADist, f32 pointBDist, Vec3f* pointA, Vec3f* pointB, Vec3f* intersect) { + f32 distDiff = pointADist - pointBDist; + + if (IS_ZERO(distDiff)) { + // both points lie on the plane. + *intersect = *pointB; + return false; + } + + if (pointADist == 0.0f) { + // pointA is on the plane + *intersect = *pointA; + } else if (pointBDist == 0.0f) { + // pointB is on the plane + *intersect = *pointB; + } else { + // place the point at the intersection point. + Math3D_LineSplitRatio(pointA, pointB, pointADist / distDiff, intersect); + } + return true; +} + +/** + * Determines if the line segment from `linePointA` to `linePointB` crosses the plane + * from `nx` + `ny` + `nz` + `originDist` = 0. If fromFront is set, then detection will only + * be true if point A crosses from the front of the plane + */ +s32 Math3D_LineSegVsPlane(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* linePointA, Vec3f* linePointB, + Vec3f* intersect, s32 fromFront) { + f32 pointADist = Math3D_PlaneF(nx, ny, nz, originDist, linePointA); + f32 pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, linePointB); + + if ((pointADist * pointBDist) > 0.0f) { + *intersect = *linePointB; + return false; + } + + if (fromFront && (pointADist < 0.0f) && (pointBDist > 0.0f)) { + *intersect = *linePointB; + return false; + } + + return Math3D_LineSegFindPlaneIntersect(pointADist, pointBDist, linePointA, linePointB, intersect); +} + +/* + * Determines if the line formed by `linePointA` and `linePointB` intersect with Triangle formed from + * vertices `v0`, `v1`, and `v2` with normal vector `nx`, `ny`, and `nz` with plane distance from origin + * `originDist` Outputs the intersection point at to `intersect` + * Returns 1 if the line intersects with the triangle, 0 otherwise + */ +s32 Math3D_TriLineIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* linePointA, + Vec3f* linePointB, Vec3f* intersect, s32 fromFront) { + + if (!Math3D_LineSegVsPlane(nx, ny, nz, originDist, linePointA, linePointB, intersect, fromFront)) { + return false; + } + + if (((nx == 0.0f) || Math3D_TriChkPointParaX(v0, v1, v2, nx, intersect->y, intersect->z)) && + ((ny == 0.0f) || Math3D_TriChkPointParaY(v0, v1, v2, ny, intersect->z, intersect->x)) && + ((nz == 0.0f) || Math3D_TriChkPointParaZ(v0, v1, v2, nz, intersect->x, intersect->y))) { + return true; + } + + *intersect = *linePointB; + return false; +} + +/* + * Creates a TriNorm output to `tri`, and calculates the normal vector and plane from vertices + * `va`, `vb`, and `vc` + */ +void Math3D_TriNorm(TriNorm* tri, Vec3f* va, Vec3f* vb, Vec3f* vc) { + tri->vtx[0] = *va; + tri->vtx[1] = *vb; + tri->vtx[2] = *vc; + + Math3D_DefPlane(va, vb, vc, &tri->plane.normal.x, &tri->plane.normal.y, &tri->plane.normal.z, + &tri->plane.originDist); +} + +/* + * Determines if point `point` lies within `sphere` + */ +s32 Math3D_PointInSph(Sphere16* sphere, Vec3f* point) { + if (Math3D_DistXYZ16toF(&sphere->center, point) < sphere->radius) { + return true; + } + + return false; +} + +/** + * Determines the distance from point (`x0`,`y0`) to the line formed from (`x1`,`y1`) and (`x2`,`y2`) + * Distance squared is output to `lineLenSq`, returns true if the point perpendicular from (`x0`,`y0`) + * is contained within the segment between (`x1`,`y1`) and (`x2`,`y2`) + */ +s32 Math3D_PointDistSqToLine2DImpl(f32 x0, f32 y0, f32 x1, f32 y1, f32 x2, f32 y2, f32* perpXOut, f32* perpYOut, + f32* lineLenSq) { + f32 perpendicularRatio; + f32 xDiff = x2 - x1; + f32 yDiff = y2 - y1; + f32 distSq = SQ(xDiff) + SQ(yDiff); + s32 ret = false; + + if (IS_ZERO(distSq)) { + *lineLenSq = 0.0f; + return false; + } + + perpendicularRatio = ((x0 - x1) * xDiff + (y0 - y1) * yDiff) / distSq; + if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) { + ret = true; + } + + *perpXOut = (xDiff * perpendicularRatio) + x1; + *perpYOut = (yDiff * perpendicularRatio) + y1; + + *lineLenSq = SQ(*perpXOut - x0) + SQ(*perpYOut - y0); + return ret; +} + +/** + * Determines the distance from point (`x0`,`y0`) to the line formed from (`x1`,`y1`) and (`x2`,`y2`) + * Distance squared is output to `lineLenSq`, returns true if the point perpendicular from (`x0`,`y0`) + * is contained within the segment between (`x1`,`y1`) and (`x2`,`y2`) + */ +s32 Math3D_PointDistSqToLine2D(f32 x0, f32 y0, f32 x1, f32 y1, f32 x2, f32 y2, f32* lineLenSq) { + f32 perpX; + f32 perpY; + + return Math3D_PointDistSqToLine2DImpl(x0, y0, x1, y1, x2, y2, &perpX, &perpY, lineLenSq); +} + +s32 Math3D_PointDistSqToLineXY(f32 x0, f32 y0, Vec3f* p1, Vec3f* p2, f32* lineLenSq) { + f32 perpendicularRatio; + f32 xDiff = p2->x - p1->x; + f32 yDiff = p2->y - p1->y; + f32 distSq = SQ(xDiff) + SQ(yDiff); + f32 perpX; + f32 perpY; + s32 ret = false; + + if (IS_ZERO(distSq)) { + *lineLenSq = 0.0f; + return false; + } + + perpendicularRatio = ((x0 - p1->x) * xDiff + (y0 - p1->y) * yDiff) / distSq; + if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) { + ret = true; + } + perpX = (xDiff * perpendicularRatio) + p1->x; + perpY = (yDiff * perpendicularRatio) + p1->y; + *lineLenSq = SQ(perpX - x0) + SQ(perpY - y0); + + return ret; +} + +s32 Math3D_PointDistSqToLineYZ(f32 y0, f32 z0, Vec3f* p1, Vec3f* p2, f32* lineLenSq) { + f32 perpendicularRatio; + f32 yDiff = p2->y - p1->y; + f32 zDiff = p2->z - p1->z; + f32 distSq = SQ(yDiff) + SQ(zDiff); + f32 perpY; + f32 perpZ; + s32 ret = false; + + if (IS_ZERO(distSq)) { + *lineLenSq = 0.0f; + return false; + } + + perpendicularRatio = ((y0 - p1->y) * yDiff + (z0 - p1->z) * zDiff) / distSq; + if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) { + ret = true; + } + perpY = (yDiff * perpendicularRatio) + p1->y; + perpZ = (zDiff * perpendicularRatio) + p1->z; + *lineLenSq = SQ(perpY - y0) + SQ(perpZ - z0); + + return ret; +} + +s32 Math3D_PointDistSqToLineZX(f32 z0, f32 x0, Vec3f* p1, Vec3f* p2, f32* lineLenSq) { + f32 perpendicularRatio; + f32 zDiff = p2->z - p1->z; + f32 xDiff = p2->x - p1->x; + f32 distSq = SQ(zDiff) + SQ(xDiff); + f32 perpZ; + f32 perpX; + s32 ret = false; + + if (IS_ZERO(distSq)) { + *lineLenSq = 0.0f; + return false; + } + + perpendicularRatio = ((z0 - p1->z) * zDiff + (x0 - p1->x) * xDiff) / distSq; + if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) { + ret = true; + } + perpZ = (zDiff * perpendicularRatio) + p1->z; + perpX = (xDiff * perpendicularRatio) + p1->x; + *lineLenSq = SQ(perpZ - z0) + SQ(perpX - x0); + + return ret; +} + +/** + * Determines if the line `line` is touching the sphere `sphere` at any point in the line. + */ +s32 Math3D_LineVsSph(Sphere16* sphere, Linef* line) { + static Vec3f sSphLinePerpendicularPoint; + Vec3f lineDiff; + f32 temp_f0_2; + f32 lineLenSq; + + if ((Math3D_PointInSph(sphere, &line->a)) || (Math3D_PointInSph(sphere, &line->b))) { + // either point of the line is in the sphere. + return true; + } + lineDiff.x = line->b.x - line->a.x; + lineDiff.y = line->b.y - line->a.y; + lineDiff.z = line->b.z - line->a.z; + + lineLenSq = SQ(lineDiff.x) + SQ(lineDiff.y) + SQ(lineDiff.z); + if (IS_ZERO(lineLenSq)) { + // line length is "0" + return false; + } + temp_f0_2 = ((((sphere->center.x - line->a.x) * lineDiff.x) + ((sphere->center.y - line->a.y) * lineDiff.y)) + + ((sphere->center.z - line->a.z) * lineDiff.z)) / + lineLenSq; + if ((temp_f0_2 < 0.0f) || (temp_f0_2 > 1.0f)) { + return false; + } + + sSphLinePerpendicularPoint.x = (lineDiff.x * temp_f0_2) + line->a.x; + sSphLinePerpendicularPoint.y = (lineDiff.y * temp_f0_2) + line->a.y; + sSphLinePerpendicularPoint.z = (lineDiff.z * temp_f0_2) + line->a.z; + + if ((SQ(sSphLinePerpendicularPoint.x - sphere->center.x) + SQ(sSphLinePerpendicularPoint.y - sphere->center.y) + + SQ(sSphLinePerpendicularPoint.z - sphere->center.z)) <= SQ((f32)sphere->radius)) { + return true; + } + return false; +} + +/** + * Gets the surface point of `sphere` intersecting with `tri` generated from the line formed from the + * sphere's surface to the midpoint of the line formed from the first two vertices of the tri + */ +void Math3D_GetSphVsTriIntersectPoint(Sphere16* sphere, TriNorm* tri, Vec3f* intersectPoint) { + static Vec3f sV0V1Center; + static Vec3f sSphereCenter; + f32 dist; + f32 splitRatio; + + sV0V1Center.x = (tri->vtx[0].x + tri->vtx[1].x) * 0.5f; + sV0V1Center.y = (tri->vtx[0].y + tri->vtx[1].y) * 0.5f; + sV0V1Center.z = (tri->vtx[0].z + tri->vtx[1].z) * 0.5f; + sSphereCenter.x = sphere->center.x; + sSphereCenter.y = sphere->center.y; + sSphereCenter.z = sphere->center.z; + dist = Math3D_Vec3f_DistXYZ(&sV0V1Center, &sSphereCenter); + // Distance from the sphere's center to the center of the line formed from v0->v1 + if (IS_ZERO(dist)) { + intersectPoint->x = sSphereCenter.x; + intersectPoint->y = sSphereCenter.y; + intersectPoint->z = sSphereCenter.z; + return; + } + splitRatio = sphere->radius / dist; + Math3D_LineSplitRatio(&sSphereCenter, &sV0V1Center, splitRatio, intersectPoint); +} + +/** + * Determines if `sphere` and `tri` and touching, and outputs the intersection point to `intersectPoint` + */ +s32 Math3D_TriVsSphIntersect(Sphere16* sphere, TriNorm* tri, Vec3f* intersectPoint) { + static Linef sTriTestLine; + static Vec3f sSphereCenter; + static Vec3f sSphPlanePos; + f32 radius; + f32 nx; + f32 ny; + f32 nz; + f32 planeDist; + + sSphereCenter.x = sphere->center.x; + sSphereCenter.y = sphere->center.y; + sSphereCenter.z = sphere->center.z; + radius = sphere->radius; + + if (!Math3D_SphCubeVsTriCube(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], &sSphereCenter, radius)) { + return false; + } + + planeDist = Math3D_UDistPlaneToPos(tri->plane.normal.x, tri->plane.normal.y, tri->plane.normal.z, + tri->plane.originDist, &sSphereCenter); + if (radius < planeDist) { + // the point that lies within the plane of the triangle which is perpendicular to the sphere's center is more + // than the radius of the sphere, the plane never crosses the sphere. + return false; + } + + // tests if any of the edges of the triangle are intersecting the sphere + sTriTestLine.a = tri->vtx[0]; + sTriTestLine.b = tri->vtx[1]; + if (Math3D_LineVsSph(sphere, &sTriTestLine)) { + Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint); + return true; + } + + sTriTestLine.a = tri->vtx[1]; + sTriTestLine.b = tri->vtx[2]; + if (Math3D_LineVsSph(sphere, &sTriTestLine)) { + Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint); + return true; + } + + sTriTestLine.a = tri->vtx[2]; + sTriTestLine.b = tri->vtx[0]; + if (Math3D_LineVsSph(sphere, &sTriTestLine)) { + Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint); + return true; + } + + nx = tri->plane.normal.x * planeDist; + ny = tri->plane.normal.y * planeDist; + nz = tri->plane.normal.z * planeDist; + + if (Math3D_PlaneF(tri->plane.normal.x, tri->plane.normal.y, tri->plane.normal.z, tri->plane.originDist, + &sSphereCenter) > 0.0f) { + sSphPlanePos.x = sSphereCenter.x - nx; + sSphPlanePos.y = sSphereCenter.y - ny; + sSphPlanePos.z = sSphereCenter.z - nz; + } else { + sSphPlanePos.x = sSphereCenter.x + nx; + sSphPlanePos.y = sSphereCenter.y + ny; + sSphPlanePos.z = sSphereCenter.z + nz; + } + + if (fabsf(tri->plane.normal.y) > 0.5f) { + if (Math3D_TriChkPointParaYDeterminate(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], sSphPlanePos.z, sSphPlanePos.x, + 0.0f, tri->plane.normal.y)) { + Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint); + return true; + } + } else if (fabsf(tri->plane.normal.x) > 0.5f) { + if (Math3D_TriChkPointParaXDeterminate(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], sSphPlanePos.y, sSphPlanePos.z, + 0.0f, tri->plane.normal.x)) { + Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint); + return true; + } + } else if (Math3D_TriChkPointParaZDeterminate(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], sSphPlanePos.x, + sSphPlanePos.y, 0.0f, tri->plane.normal.z)) { + Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint); + return true; + } + return false; +} + +/* + * Checks if point `point` is within cylinder `cyl` + * Returns 1 if the point is inside the cylinder, 0 otherwise. + */ +s32 Math3D_PointInCyl(Cylinder16* cyl, Vec3f* point) { + f32 bottom; + f32 top; + f32 x = cyl->pos.x - point->x; + f32 z = cyl->pos.z - point->z; + + bottom = (f32)cyl->pos.y + cyl->yShift; + top = cyl->height + bottom; + + if ((SQ(x) + SQ(z)) < SQ(cyl->radius) && (bottom < point->y) && (point->y < top)) { + return true; + } else { + return false; + } +} + +s32 Math3D_CylVsLineSeg(Cylinder16* cyl, Vec3f* linePointA, Vec3f* linePointB, Vec3f* intersectA, Vec3f* intersectB) { + Vec3f cylToPtA; + Vec3f cylToPtB; + Vec3f ptAToPtB; + f32 fracA; + f32 fracB; + f32 fracBase; + f32 zero; + f32 pad; + f32 cylRadiusSq; + f32 radSqDiff; + f32 distCent2; + f32 dot2AB; + s32 sideIntA; + s32 sideIntB; + s32 intBeyondA; + s32 intBeyondB; + s32 intFlags; + Vec3f intPts[4]; + s32 count; + s32 i; + + fracA = 0.0f; + fracB = 0.0f; + +//! FAKE: +dummy:; + + zero = 0.0f; + intFlags = 0; + + if (Math3D_PointInCyl(cyl, linePointA) && Math3D_PointInCyl(cyl, linePointB)) { + // both points are in the cylinder + *intersectA = *linePointA; + *intersectB = *linePointB; + return 2; + } + + cylToPtA.x = linePointA->x - cyl->pos.x; + cylToPtA.y = linePointA->y - cyl->pos.y - cyl->yShift; + cylToPtA.z = linePointA->z - cyl->pos.z; + cylToPtB.x = linePointB->x - cyl->pos.x; + cylToPtB.y = linePointB->y - cyl->pos.y - cyl->yShift; + cylToPtB.z = linePointB->z - cyl->pos.z; + Math_Vec3f_Diff(&cylToPtB, &cylToPtA, &ptAToPtB); + cylRadiusSq = SQ(cyl->radius); + + /** + * This section checks for intersections with the cylinder's base and top + */ + if (!IS_ZERO(ptAToPtB.y)) { + // fraction of length along AB to reach y = 0 + fracBase = -cylToPtA.y / ptAToPtB.y; + if ((fracBase >= 0.0f) && (fracBase <= 1.0f)) { + f32 baseIntX = (ptAToPtB.x * fracBase) + cylToPtA.x; + f32 baseIntZ = (ptAToPtB.z * fracBase) + cylToPtA.z; + + if ((SQ(baseIntX) + SQ(baseIntZ)) < cylRadiusSq) { + // adds base intersection point to intPts and sets its flag + intPts[0].x = cyl->pos.x + baseIntX; + intPts[0].y = (f32)cyl->pos.y + cyl->yShift; + intPts[0].z = cyl->pos.z + baseIntZ; + intFlags |= 1; + } + } + // fraction of length along AB to reach y = cyl->height + fracA = (cyl->height - cylToPtA.y) / ptAToPtB.y; + if ((fracA >= 0.0f) && (fracA <= 1.0f)) { + f32 topIntX = ptAToPtB.x * fracA + cylToPtA.x; + f32 topIntZ = ptAToPtB.z * fracA + cylToPtA.z; + + if ((SQ(topIntX) + SQ(topIntZ)) < cylRadiusSq) { + // adds top intersection point to intPts and sets its flag + intPts[1].x = cyl->pos.x + topIntX; + intPts[1].y = (f32)cyl->pos.y + cyl->yShift + cyl->height; + intPts[1].z = cyl->pos.z + topIntZ; + intFlags |= 2; + } + } + } + + /** + * This section finds the points of intersection of the infinite line containing AB with the side of the infinite + * cylinder containing cyl. Intersection points beyond the bounds of the segment and cylinder are filtered out + * afterward. + */ + radSqDiff = SQXZ(cylToPtA) - cylRadiusSq; + if (!IS_ZERO(2.0f * SQXZ(ptAToPtB))) { + dot2AB = 2.0f * DOTXZ(ptAToPtB, cylToPtA); + if (SQ(dot2AB) < (4.0f * SQXZ(ptAToPtB) * radSqDiff)) { + // Line's closest xz-approach is outside cylinder. No intersections. + return 0; + } + if ((SQ(dot2AB) - (4.0f * SQXZ(ptAToPtB) * radSqDiff)) > zero) { + sideIntA = sideIntB = 1; + } else { + // Line is tangent in xz-plane. At most 1 side intersection. + sideIntA = 1; + sideIntB = 0; + } + distCent2 = sqrtf(SQ(dot2AB) - (4.0f * SQXZ(ptAToPtB) * radSqDiff)); + if (sideIntA != 0) { + // fraction of length along AB for side intersection closer to A + fracA = (distCent2 - dot2AB) / (2.0f * SQXZ(ptAToPtB)); + } + if (sideIntB != 0) { + // fraction of length along AB for side intersection closer to B + fracB = (-dot2AB - distCent2) / (2.0f * SQXZ(ptAToPtB)); + } + } else if (!IS_ZERO(2.0f * DOTXZ(ptAToPtB, cylToPtA))) { + // Used if the line segment is nearly vertical. Unclear what it's calculating. + fracA = -radSqDiff / (2.0f * DOTXZ(ptAToPtB, cylToPtA)); + sideIntA = 1; + sideIntB = 0; + } else { + return 0; + } + + // checks for intersection points outside the bounds of the segment + if (!sideIntB) { + if ((fracA < 0.0f) || (fracA > 1.0f)) { + return 0; + } + } else { + intBeyondA = (fracA < 0.0f) || (fracA > 1.0f); + intBeyondB = (fracB < 0.0f) || (fracB > 1.0f); + if (intBeyondA && intBeyondB) { + return 0; + } + if (intBeyondA) { + sideIntA = 0; + } + if (intBeyondB) { + sideIntB = 0; + } + } + + // checks for intersection points outside the bounds of the cylinder + if ((sideIntA != 0) && + (((fracA * ptAToPtB.y + cylToPtA.y) < 0.0f) || (cyl->height < (fracA * ptAToPtB.y + cylToPtA.y)))) { + sideIntA = 0; + } + if ((sideIntB != 0) && + (((fracB * ptAToPtB.y + cylToPtA.y) < 0.0f) || (cyl->height < (fracB * ptAToPtB.y + cylToPtA.y)))) { + sideIntB = 0; + } + if ((sideIntA == 0) && (sideIntB == 0)) { + return 0; + } + + // Adds intersection points to intPts and sets side A and side B flags + if (sideIntA != 0 && sideIntB != 0) { + intPts[2].x = (fracA * ptAToPtB.x + cylToPtA.x) + cyl->pos.x; + intPts[2].y = (fracA * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift; + intPts[2].z = (fracA * ptAToPtB.z + cylToPtA.z) + cyl->pos.z; + intFlags |= 4; + intPts[3].x = (fracB * ptAToPtB.x + cylToPtA.x) + cyl->pos.x; + intPts[3].y = (fracB * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift; + intPts[3].z = (fracB * ptAToPtB.z + cylToPtA.z) + cyl->pos.z; + intFlags |= 8; + } else if (sideIntA != 0) { + intPts[2].x = (fracA * ptAToPtB.x + cylToPtA.x) + cyl->pos.x; + intPts[2].y = (fracA * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift; + intPts[2].z = (fracA * ptAToPtB.z + cylToPtA.z) + cyl->pos.z; + intFlags |= 4; + } else if (sideIntB != 0) { + intPts[2].x = (fracB * ptAToPtB.x + cylToPtA.x) + cyl->pos.x; + intPts[2].y = (fracB * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift; + intPts[2].z = (fracB * ptAToPtB.z + cylToPtA.z) + cyl->pos.z; + intFlags |= 4; + } + + /** + * Places the found intersection points into intersectA and intersectB. IntersectA is always closer to point A + */ + for (count = 0, i = 0; i < ARRAY_COUNT(intPts); i++) { + if (intFlags & (1 << i)) { + if (count == 0) { + *intersectA = intPts[i]; + } else if (count == 1) { + if (Math3D_Vec3fDistSq(intersectA, linePointA) < Math3D_Vec3fDistSq(intersectA, &intPts[i])) { + *intersectB = intPts[i]; + } else { + *intersectB = *intersectA; + *intersectA = intPts[i]; + } + break; + } + count++; + } + } + return count; +} + +/* + * Determines if `cyl` and `tri` are touching. The point of intersection + * is placed in `intersect` Returns 1 if they are touching, 0 otherwise. + */ +s32 Math3D_CylTriVsIntersect(Cylinder16* cyl, TriNorm* tri, Vec3f* intersect) { + static Sphere16 sTopSphere; + static Sphere16 sBottomSphere; + static Vec3f sCylIntersectA; + static Vec3f sCylIntersectB; + f32 yIntersect; + f32 cylTop; + f32 cylBottom; + f32 minDistSq; + f32 radiusTodistFromCylYIntersectTov0v1; + f32 distFromPointAToIntersectASq; + Vec3f cylIntersectCenter; + + cylBottom = (f32)cyl->pos.y + cyl->yShift; + cylTop = cyl->height + cylBottom; + + if (((tri->vtx[0].y < cylBottom) && (tri->vtx[1].y < cylBottom) && (tri->vtx[2].y < cylBottom)) || + ((cylTop < tri->vtx[0].y) && (cylTop < tri->vtx[1].y) && (cylTop < tri->vtx[2].y))) { + // If all of the vertices are below or all of the vertices are above the cylinder. + return false; + } + + minDistSq = 1.e38f; + if (Math3D_CylVsLineSeg(cyl, &tri->vtx[0], &tri->vtx[1], &sCylIntersectA, &sCylIntersectB)) { + distFromPointAToIntersectASq = Math3D_Vec3fDistSq(&sCylIntersectA, &tri->vtx[0]); + minDistSq = distFromPointAToIntersectASq; + *intersect = sCylIntersectA; + } + + if (Math3D_CylVsLineSeg(cyl, &tri->vtx[2], &tri->vtx[1], &sCylIntersectA, &sCylIntersectB)) { + distFromPointAToIntersectASq = Math3D_Vec3fDistSq(&sCylIntersectA, &tri->vtx[2]); + if (distFromPointAToIntersectASq < minDistSq) { + *intersect = sCylIntersectA; + minDistSq = distFromPointAToIntersectASq; + } + } + + if (Math3D_CylVsLineSeg(cyl, &tri->vtx[0], &tri->vtx[2], &sCylIntersectA, &sCylIntersectB)) { + distFromPointAToIntersectASq = Math3D_Vec3fDistSq(&sCylIntersectA, &tri->vtx[0]); + if (distFromPointAToIntersectASq < minDistSq) { + *intersect = sCylIntersectA; + minDistSq = distFromPointAToIntersectASq; + } + } + + if (minDistSq != 1.e38f) { + return true; + } + + if (Math3D_TriChkLineSegParaYIntersect(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], tri->plane.normal.x, + tri->plane.normal.y, tri->plane.normal.z, tri->plane.originDist, cyl->pos.z, + cyl->pos.x, &yIntersect, cylBottom, cylTop)) { + Vec3f midpointv0v1; + Vec3f diffMidpointIntersect; + f32 distFromCylYIntersectTov0v1; + s32 pad; + + cylIntersectCenter.x = cyl->pos.x; + cylIntersectCenter.y = yIntersect; + cylIntersectCenter.z = cyl->pos.z; + + midpointv0v1.x = (tri->vtx[0].x + tri->vtx[1].x) * 0.5f; + midpointv0v1.y = (tri->vtx[0].y + tri->vtx[1].y) * 0.5f; + midpointv0v1.z = (tri->vtx[0].z + tri->vtx[1].z) * 0.5f; + + Math_Vec3f_Diff(&midpointv0v1, &cylIntersectCenter, &diffMidpointIntersect); + distFromCylYIntersectTov0v1 = sqrtf(SQ(diffMidpointIntersect.x) + SQ(diffMidpointIntersect.z)); + + if (IS_ZERO(distFromCylYIntersectTov0v1)) { + Math_Vec3f_Copy(intersect, &midpointv0v1); + return true; + } + + radiusTodistFromCylYIntersectTov0v1 = cyl->radius / distFromCylYIntersectTov0v1; + Math3D_PointOnDirectedLine(&cylIntersectCenter, &diffMidpointIntersect, radiusTodistFromCylYIntersectTov0v1, + intersect); + return true; + } + + sTopSphere.center.x = sBottomSphere.center.x = cyl->pos.x; + sTopSphere.center.z = sBottomSphere.center.z = cyl->pos.z; + sTopSphere.center.y = cylTop; + sBottomSphere.center.y = cylBottom; + sTopSphere.radius = sBottomSphere.radius = cyl->radius; + + if (Math3D_TriVsSphIntersect(&sTopSphere, tri, intersect) || + Math3D_TriVsSphIntersect(&sBottomSphere, tri, intersect)) { + return true; + } + return false; +} + +/* + * Determines if `cyl` and `tri` are touching. + */ +s32 Math3D_CylVsTri(Cylinder16* cyl, TriNorm* tri) { + Vec3f intersect; + + return Math3D_CylTriVsIntersect(cyl, tri, &intersect); +} + +/* + * Determines if two spheres are touching. + */ +s32 Math3D_SphVsSph(Sphere16* sphereA, Sphere16* sphereB) { + f32 overlapSize; + + return Math3D_SphVsSphOverlap(sphereA, sphereB, &overlapSize); +} + +/* + * Determines if two spheres are touching. The amount that they're overlapping is placed in `overlapSize` + */ +s32 Math3D_SphVsSphOverlap(Sphere16* sphereA, Sphere16* sphereB, f32* overlapSize) { + f32 centerDist; + + return Math3D_SphVsSphOverlapCenterDist(sphereA, sphereB, overlapSize, ¢erDist); +} + +/* + * Determines if two spheres are touching The distance from the centers is placed in `centerDist`, + * and the amount that they're overlapping is placed in `overlapSize` + */ +s32 Math3D_SphVsSphOverlapCenterDist(Sphere16* sphereA, Sphere16* sphereB, f32* overlapSize, f32* centerDist) { + Vec3f diff; + + diff.x = (f32)sphereA->center.x - (f32)sphereB->center.x; + diff.y = (f32)sphereA->center.y - (f32)sphereB->center.y; + diff.z = (f32)sphereA->center.z - (f32)sphereB->center.z; + + *centerDist = sqrtf(SQ(diff.x) + SQ(diff.y) + SQ(diff.z)); + + *overlapSize = (((f32)sphereA->radius + (f32)sphereB->radius) - *centerDist); + if (*overlapSize > 0.008f) { + return true; + } + + *overlapSize = 0.0f; + return false; +} + +/** + * Checks if `sph` and `cyl` are touching, output the amount of xz overlap to `overlapSize` + */ +s32 Math3D_SphVsCylOverlap(Sphere16* sph, Cylinder16* cyl, f32* overlapSize) { + f32 centerDist; + + return Math3D_SphVsCylOverlapCenterDist(sph, cyl, overlapSize, ¢erDist); +} + +/** + * Checks if `sph` and `cyl` are touching, output the xz distance of the centers to `centerDist`, and the amount of + * xz overlap to `overlapSize` + */ +s32 Math3D_SphVsCylOverlapCenterDist(Sphere16* sph, Cylinder16* cyl, f32* overlapSize, f32* centerDist) { + static Cylinderf sCylf; + static Spheref sSphf; + f32 x; + f32 z; + f32 combinedRadius; + f32 cylBottom; + f32 cylTop; + f32 sphBottom; + f32 sphTop; + + if ((sph->radius <= 0) || (cyl->radius <= 0)) { + // either radius is 0 + return false; + } + sSphf.center.y = sph->center.y; + sSphf.radius = sph->radius; + sCylf.pos.y = cyl->pos.y; + sCylf.yShift = cyl->yShift; + sCylf.height = cyl->height; + x = (f32)sph->center.x - cyl->pos.x; + z = (f32)sph->center.z - cyl->pos.z; + combinedRadius = (f32)sph->radius + cyl->radius; + *centerDist = sqrtf(SQ(x) + SQ(z)); + if (combinedRadius < *centerDist) { + // if the combined radii is less than the distance to the centers, they cannot be touching. + return false; + } + + cylBottom = (sCylf.pos.y + sCylf.yShift); + cylTop = cylBottom + sCylf.height; + sphBottom = sSphf.center.y - sSphf.radius; + sphTop = sSphf.center.y + sSphf.radius; + + if ((sphTop >= cylBottom) && (sphBottom <= cylTop)) { + // if the cylinder and sphere are intersecting on the xz plane, check if they're intersecting on + // the y axis. + *overlapSize = combinedRadius - *centerDist; + return true; + } + return false; +} + +/** + * Checks if `ca` and `cb` are touching, output the amount of xz overlap to `overlapSize` + */ +s32 Math3D_CylVsCylOverlap(Cylinder16* ca, Cylinder16* cb, f32* overlapSize) { + f32 centerDist; + + return Math3D_CylVsCylOverlapCenterDist(ca, cb, overlapSize, ¢erDist); +} + +/** + * Checks if `ca` and `cb` are touching, output the xz distance of the centers to `centerDist`, and the amount of + * xz overlap to `overlapSize` + */ +s32 Math3D_CylVsCylOverlapCenterDist(Cylinder16* ca, Cylinder16* cb, f32* overlapSize, f32* centerDist) { + static Cylinderf sCaf; + static Cylinderf sCbf; + + Math_Vec3s_ToVec3f(&sCaf.pos, &ca->pos); + sCaf.radius = ca->radius; + sCaf.yShift = ca->yShift; + sCaf.height = ca->height; + + Math_Vec3s_ToVec3f(&sCbf.pos, &cb->pos); + sCbf.radius = cb->radius; + sCbf.yShift = cb->yShift; + sCbf.height = cb->height; + + *centerDist = sqrtf(SQ(sCaf.pos.x - sCbf.pos.x) + SQ(sCaf.pos.z - sCbf.pos.z)); + + // The combined radii are within the xz distance + if ((sCaf.radius + sCbf.radius) < *centerDist) { + return false; + } + + // top of ca < bottom of cb or top of cb < bottom of ca + if ((((sCaf.pos.y + sCaf.yShift) + sCaf.height) < (sCbf.pos.y + sCbf.yShift)) || + (((sCbf.pos.y + sCbf.yShift) + sCbf.height) < (sCaf.pos.y + sCaf.yShift))) { + return false; + } + + *overlapSize = sCaf.radius + sCbf.radius - *centerDist; + return true; +} + +/* + * Determines if triangle `ta` intersects with triangle `tb` the point of + * intersection is output to `intersect. + * Returns true is the triangles intersect, 0 otherwise + */ +s32 Math3D_TriVsTriIntersect(TriNorm* ta, TriNorm* tb, Vec3f* intersect) { + f32 dist0 = Math3D_Plane(&ta->plane, &tb->vtx[0]); + f32 dist1 = Math3D_Plane(&ta->plane, &tb->vtx[1]); + f32 dist2 = Math3D_Plane(&ta->plane, &tb->vtx[2]); + + if (((dist0 > 0.0f) && (dist1 > 0.0f) && (dist2 > 0.0f)) || + (((dist0 < 0.0f) && (dist1 < 0.0f)) && (dist2 < 0.0f))) { + return false; + } + + dist0 = Math3D_Plane(&tb->plane, &ta->vtx[0]); + dist1 = Math3D_Plane(&tb->plane, &ta->vtx[1]); + dist2 = Math3D_Plane(&tb->plane, &ta->vtx[2]); + + if ((((dist0 > 0.0f) && (dist1 > 0.0f)) && (dist2 > 0.0f)) || + ((dist0 < 0.0f) && (dist1 < 0.0f) && (dist2 < 0.0f))) { + return false; + } + + if (Math3D_TriLineIntersect(&tb->vtx[0], &tb->vtx[1], &tb->vtx[2], tb->plane.normal.x, tb->plane.normal.y, + tb->plane.normal.z, tb->plane.originDist, &ta->vtx[0], &ta->vtx[1], intersect, 0)) { + return true; + } + if (Math3D_TriLineIntersect(&tb->vtx[0], &tb->vtx[1], &tb->vtx[2], tb->plane.normal.x, tb->plane.normal.y, + tb->plane.normal.z, tb->plane.originDist, &ta->vtx[1], &ta->vtx[2], intersect, 0)) { + return true; + } + if (Math3D_TriLineIntersect(&tb->vtx[0], &tb->vtx[1], &tb->vtx[2], tb->plane.normal.x, tb->plane.normal.y, + tb->plane.normal.z, tb->plane.originDist, &ta->vtx[2], &ta->vtx[0], intersect, 0)) { + return true; + } + if (Math3D_TriLineIntersect(&ta->vtx[0], &ta->vtx[1], &ta->vtx[2], ta->plane.normal.x, ta->plane.normal.y, + ta->plane.normal.z, ta->plane.originDist, &tb->vtx[0], &tb->vtx[1], intersect, 0)) { + return true; + } + if (Math3D_TriLineIntersect(&ta->vtx[0], &ta->vtx[1], &ta->vtx[2], ta->plane.normal.x, ta->plane.normal.y, + ta->plane.normal.z, ta->plane.originDist, &tb->vtx[1], &tb->vtx[2], intersect, 0)) { + return true; + } + if (Math3D_TriLineIntersect(&ta->vtx[0], &ta->vtx[1], &ta->vtx[2], ta->plane.normal.x, ta->plane.normal.y, + ta->plane.normal.z, ta->plane.originDist, &tb->vtx[2], &tb->vtx[0], intersect, 0)) { + return true; + } + return false; +} + +s32 Math3D_XZInSphere(Sphere16* sphere, f32 x, f32 z) { + f32 xDiff = sphere->center.x - x; + f32 zDiff = sphere->center.z - z; + + if ((SQ(xDiff) + SQ(zDiff)) <= SQ(sphere->radius)) { + return true; + } + return false; +} + +s32 Math3D_XYInSphere(Sphere16* sphere, f32 x, f32 y) { + f32 xDiff = sphere->center.x - x; + f32 yDiff = sphere->center.y - y; + + if ((SQ(xDiff) + SQ(yDiff)) <= SQ(sphere->radius)) { + return true; + } + return false; +} + +s32 Math3D_YZInSphere(Sphere16* sphere, f32 y, f32 z) { + f32 yDiff = sphere->center.y - y; + f32 zDiff = sphere->center.z - z; + + if ((SQ(yDiff) + SQ(zDiff)) <= SQ(sphere->radius)) { + return true; + } + return false; +} + +/** + * @brief Computes the intersection points, if any, of the circle of radius radius, center (centerX, centerY) with the + * line through the point (pointX, pointY) in direction (dirX, dirY). + * + * @param[in] centreX x coordinate of centre of circle + * @param[in] centerY y coordinate of centre of circle + * @param[in] radius of circle + * @param[in] pointX x coordinate of point on line + * @param[in] pointY y coordinate of point on line + * @param[in] dirX x value of direction vector of line + * @param[in] dirY y value of direction vecotr of line + * @param[out] intersectAX x coordinate of first intersection + * @param[out] intersectAY y coordinate of first intersection + * @param[out] intersectBX x coordinate of second intersection + * @param[out] intersectBY y coordinate of second intersection + * @return number of intersections(ish) + */ +s32 Math3D_CircleLineIntersections(f32 centreX, f32 centerY, f32 radius, f32 pointX, f32 pointY, f32 dirX, f32 dirY, + f32* intersectAX, f32* intersectAY, f32* intersectBX, f32* intersectBY) { + f32 a = SQ(dirX) + SQ(dirY); // t^2 coefficient, |dir|^2 + f32 diffX = pointX - centreX; + f32 diffY = pointY - centerY; + f32 b; // t coefficient + f32 delta; // discriminant of quadratic + f32 rootP; // larger root of quadratic + f32 rootN; // smaller root of quadratic + s32 ret; + + // if the direction vector's magnitude is too small, assume no intersections + if ((IS_ZERO(dirX) && IS_ZERO(dirY)) || IS_ZERO(a)) { + *intersectAX = 0.0f; + *intersectAY = 0.0f; + *intersectBX = 0.0f; + *intersectBY = 0.0f; + return 0; + } + + b = 2.0f * (dirX * diffX + dirY * diffY); // 2 dir . (point - centre) + delta = SQ(b) - 4.0f * a * (SQ(diffX) + SQ(diffY) - SQ(radius)); + ret = 0; + + if (IS_ZERO(delta)) { // At most one root if discriminant is close to zero + // This root is always overwritten later. + rootN = -b / (2.0f * a); + *intersectAX = dirX * rootN + pointX; + *intersectAY = dirY * rootN + pointY; + + *intersectBX = 0.0f; + *intersectBY = 0.0f; + } + + if (delta > 0.0f) { // Two roots if discriminant > 0 + rootN = (-b - sqrtf(delta)) / (2.0f * a); + *intersectAX = dirX * rootN + pointX; + *intersectAY = dirY * rootN + pointY; + + rootP = (-b + sqrtf(delta)) / (2.0f * a); + *intersectBX = dirX * rootP + pointX; + *intersectBY = dirY * rootP + pointY; + + ret = 2; + } else { // "No roots if discriminant <= 0.0f"* + //! @bug Should be one root if discriminant == 0, not zero (although this case is unlikely for floats) + *intersectAX = 0.0f; + *intersectAY = 0.0f; + } + + return ret; +} + +void func_8017FD44(Vec3f* arg0, Vec3f* arg1, Vec3f* dst, f32 arg3) { + Vec3f sp2C; + s16 sp2A; + f32 sp24; + + if ((arg3 < -1.0f) && (arg3 > 1.0f)) { + return; + } + + sp2C.x = (arg0->x + arg1->x) / 2.0f; + sp2C.z = (arg0->z + arg1->z) / 2.0f; + sp24 = sqrtf(SQ(sp2C.x - arg0->x) + SQ(sp2C.z - arg0->z)); + dst->y = (arg1->y - arg0->y) * arg3 + arg0->y; + sp2A = Math_Vec3f_Yaw(&sp2C, arg0); + dst->x = Math_SinS(TRUNCF_BINANG(0x7FFF * arg3) + sp2A) * sp24 + sp2C.x; + dst->z = Math_CosS(TRUNCF_BINANG(0x7FFF * arg3) + sp2A) * sp24 + sp2C.z; +} |