#include "Vectors.h" #include "ExtMath.h" #include "Funcs.h" #include "Constants.h" #include "Core.h" void Vec3_Lerp(Vec3* result, const Vec3* a, const Vec3* b, float blend) { result->x = blend * (b->x - a->x) + a->x; result->y = blend * (b->y - a->y) + a->y; result->z = blend * (b->z - a->z) + a->z; } void Vec3_Normalise(Vec3* v) { float scale, lenSquared; lenSquared = v->x * v->x + v->y * v->y + v->z * v->z; /* handle zero vector */ if (!lenSquared) return; scale = 1.0f / Math_SqrtF(lenSquared); v->x = v->x * scale; v->y = v->y * scale; v->z = v->z * scale; } void Vec3_Transform(Vec3* result, const Vec3* a, const struct Matrix* mat) { /* a could be pointing to result - therefore can't directly assign X/Y/Z */ float x = a->x * mat->row1.x + a->y * mat->row2.x + a->z * mat->row3.x + mat->row4.x; float y = a->x * mat->row1.y + a->y * mat->row2.y + a->z * mat->row3.y + mat->row4.y; float z = a->x * mat->row1.z + a->y * mat->row2.z + a->z * mat->row3.z + mat->row4.z; result->x = x; result->y = y; result->z = z; } void Vec3_TransformY(Vec3* result, float y, const struct Matrix* mat) { result->x = y * mat->row2.x + mat->row4.x; result->y = y * mat->row2.y + mat->row4.y; result->z = y * mat->row2.z + mat->row4.z; } Vec3 Vec3_RotateX(Vec3 v, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); return Vec3_Create3(v.x, cosA * v.y + sinA * v.z, -sinA * v.y + cosA * v.z); } Vec3 Vec3_RotateY(Vec3 v, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); return Vec3_Create3(cosA * v.x - sinA * v.z, v.y, sinA * v.x + cosA * v.z); } Vec3 Vec3_RotateY3(float x, float y, float z, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); return Vec3_Create3(cosA * x - sinA * z, y, sinA * x + cosA * z); } Vec3 Vec3_RotateZ(Vec3 v, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); return Vec3_Create3(cosA * v.x + sinA * v.y, -sinA * v.x + cosA * v.y, v.z); } void IVec3_Floor(IVec3* result, const Vec3* a) { result->x = Math_Floor(a->x); result->y = Math_Floor(a->y); result->z = Math_Floor(a->z); } void IVec3_ToVec3(Vec3* result, const IVec3* a) { result->x = (float)a->x; result->y = (float)a->y; result->z = (float)a->z; } void IVec3_Min(IVec3* result, const IVec3* a, const IVec3* b) { result->x = min(a->x, b->x); result->y = min(a->y, b->y); result->z = min(a->z, b->z); } void IVec3_Max(IVec3* result, const IVec3* a, const IVec3* b) { result->x = max(a->x, b->x); result->y = max(a->y, b->y); result->z = max(a->z, b->z); } Vec3 Vec3_GetDirVector(float yawRad, float pitchRad) { float x = -Math_CosF(pitchRad) * -Math_SinF(yawRad); float y = -Math_SinF(pitchRad); float z = -Math_CosF(pitchRad) * Math_CosF(yawRad); return Vec3_Create3(x, y, z); } /*void Vec3_GetHeading(Vector3 dir, float* yaw, float* pitch) { *pitch = (float)Math_Asin(-dir.y); *yaw = (float)Math_Atan2(dir.x, -dir.z); }*/ const struct Matrix Matrix_Identity = Matrix_IdentityValue; /* Transposed, source https://open.gl/transformations */ void Matrix_RotateX(struct Matrix* result, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); *result = Matrix_Identity; result->row2.y = cosA; result->row2.z = sinA; result->row3.y = -sinA; result->row3.z = cosA; } void Matrix_RotateY(struct Matrix* result, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); *result = Matrix_Identity; result->row1.x = cosA; result->row1.z = -sinA; result->row3.x = sinA; result->row3.z = cosA; } void Matrix_RotateZ(struct Matrix* result, float angle) { float cosA = Math_CosF(angle); float sinA = Math_SinF(angle); *result = Matrix_Identity; result->row1.x = cosA; result->row1.y = sinA; result->row2.x = -sinA; result->row2.y = cosA; } void Matrix_Translate(struct Matrix* result, float x, float y, float z) { *result = Matrix_Identity; result->row4.x = x; result->row4.y = y; result->row4.z = z; } void Matrix_Scale(struct Matrix* result, float x, float y, float z) { *result = Matrix_Identity; result->row1.x = x; result->row2.y = y; result->row3.z = z; } void Matrix_Mul(struct Matrix* result, const struct Matrix* left, const struct Matrix* right) { /* Originally from http://www.edais.co.uk/blog/?p=27 */ float lM11 = left->row1.x, lM12 = left->row1.y, lM13 = left->row1.z, lM14 = left->row1.w, lM21 = left->row2.x, lM22 = left->row2.y, lM23 = left->row2.z, lM24 = left->row2.w, lM31 = left->row3.x, lM32 = left->row3.y, lM33 = left->row3.z, lM34 = left->row3.w, lM41 = left->row4.x, lM42 = left->row4.y, lM43 = left->row4.z, lM44 = left->row4.w, rM11 = right->row1.x, rM12 = right->row1.y, rM13 = right->row1.z, rM14 = right->row1.w, rM21 = right->row2.x, rM22 = right->row2.y, rM23 = right->row2.z, rM24 = right->row2.w, rM31 = right->row3.x, rM32 = right->row3.y, rM33 = right->row3.z, rM34 = right->row3.w, rM41 = right->row4.x, rM42 = right->row4.y, rM43 = right->row4.z, rM44 = right->row4.w; result->row1.x = (((lM11 * rM11) + (lM12 * rM21)) + (lM13 * rM31)) + (lM14 * rM41); result->row1.y = (((lM11 * rM12) + (lM12 * rM22)) + (lM13 * rM32)) + (lM14 * rM42); result->row1.z = (((lM11 * rM13) + (lM12 * rM23)) + (lM13 * rM33)) + (lM14 * rM43); result->row1.w = (((lM11 * rM14) + (lM12 * rM24)) + (lM13 * rM34)) + (lM14 * rM44); result->row2.x = (((lM21 * rM11) + (lM22 * rM21)) + (lM23 * rM31)) + (lM24 * rM41); result->row2.y = (((lM21 * rM12) + (lM22 * rM22)) + (lM23 * rM32)) + (lM24 * rM42); result->row2.z = (((lM21 * rM13) + (lM22 * rM23)) + (lM23 * rM33)) + (lM24 * rM43); result->row2.w = (((lM21 * rM14) + (lM22 * rM24)) + (lM23 * rM34)) + (lM24 * rM44); result->row3.x = (((lM31 * rM11) + (lM32 * rM21)) + (lM33 * rM31)) + (lM34 * rM41); result->row3.y = (((lM31 * rM12) + (lM32 * rM22)) + (lM33 * rM32)) + (lM34 * rM42); result->row3.z = (((lM31 * rM13) + (lM32 * rM23)) + (lM33 * rM33)) + (lM34 * rM43); result->row3.w = (((lM31 * rM14) + (lM32 * rM24)) + (lM33 * rM34)) + (lM34 * rM44); result->row4.x = (((lM41 * rM11) + (lM42 * rM21)) + (lM43 * rM31)) + (lM44 * rM41); result->row4.y = (((lM41 * rM12) + (lM42 * rM22)) + (lM43 * rM32)) + (lM44 * rM42); result->row4.z = (((lM41 * rM13) + (lM42 * rM23)) + (lM43 * rM33)) + (lM44 * rM43); result->row4.w = (((lM41 * rM14) + (lM42 * rM24)) + (lM43 * rM34)) + (lM44 * rM44); } void Matrix_LookRot(struct Matrix* result, Vec3 pos, Vec2 rot) { struct Matrix rotX, rotY, trans; Matrix_RotateX(&rotX, rot.y); Matrix_RotateY(&rotY, rot.x); Matrix_Translate(&trans, -pos.x, -pos.y, -pos.z); Matrix_Mul(result, &rotY, &rotX); Matrix_Mul(result, &trans, result); } /* TODO: Move to matrix instance instead */ static float frustum00, frustum01, frustum02, frustum03, frustum10, frustum11, frustum12, frustum13, frustum20, frustum21, frustum22, frustum23, frustum30, frustum31, frustum32, frustum33, frustum40, frustum41, frustum42, frustum43; static void FrustumCulling_Normalise(float* plane0, float* plane1, float* plane2, float* plane3) { float val1 = *plane0, val2 = *plane1, val3 = *plane2; float t = Math_SqrtF(val1 * val1 + val2 * val2 + val3 * val3); *plane0 /= t; *plane1 /= t; *plane2 /= t; *plane3 /= t; } cc_bool FrustumCulling_SphereInFrustum(float x, float y, float z, float radius) { float d = frustum00 * x + frustum01 * y + frustum02 * z + frustum03; if (d <= -radius) return false; d = frustum10 * x + frustum11 * y + frustum12 * z + frustum13; if (d <= -radius) return false; d = frustum20 * x + frustum21 * y + frustum22 * z + frustum23; if (d <= -radius) return false; d = frustum30 * x + frustum31 * y + frustum32 * z + frustum33; if (d <= -radius) return false; d = frustum40 * x + frustum41 * y + frustum42 * z + frustum43; if (d <= -radius) return false; /* Don't test NEAR plane, it's pointless */ return true; } void FrustumCulling_CalcFrustumEquations(struct Matrix* projection, struct Matrix* modelView) { struct Matrix clip; Matrix_Mul(&clip, modelView, projection); /* Extract the RIGHT plane */ frustum00 = clip.row1.w - clip.row1.x; frustum01 = clip.row2.w - clip.row2.x; frustum02 = clip.row3.w - clip.row3.x; frustum03 = clip.row4.w - clip.row4.x; FrustumCulling_Normalise(&frustum00, &frustum01, &frustum02, &frustum03); /* Extract the LEFT plane */ frustum10 = clip.row1.w + clip.row1.x; frustum11 = clip.row2.w + clip.row2.x; frustum12 = clip.row3.w + clip.row3.x; frustum13 = clip.row4.w + clip.row4.x; FrustumCulling_Normalise(&frustum10, &frustum11, &frustum12, &frustum13); /* Extract the BOTTOM plane */ frustum20 = clip.row1.w + clip.row1.y; frustum21 = clip.row2.w + clip.row2.y; frustum22 = clip.row3.w + clip.row3.y; frustum23 = clip.row4.w + clip.row4.y; FrustumCulling_Normalise(&frustum20, &frustum21, &frustum22, &frustum23); /* Extract the TOP plane */ frustum30 = clip.row1.w - clip.row1.y; frustum31 = clip.row2.w - clip.row2.y; frustum32 = clip.row3.w - clip.row3.y; frustum33 = clip.row4.w - clip.row4.y; FrustumCulling_Normalise(&frustum30, &frustum31, &frustum32, &frustum33); /* Extract the FAR plane (Different for each graphics backend) */ #if (CC_GFX_BACKEND == CC_GFX_BACKEND_D3D9) || (CC_GFX_BACKEND == CC_GFX_BACKEND_D3D11) /* OpenGL and Direct3D require slightly different behaviour for NEAR clipping planes */ /* https://www.gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf */ /* (and because reverse Z is used, 'NEAR' plane is actually the 'FAR' clipping plane) */ frustum40 = clip.row1.z; frustum41 = clip.row2.z; frustum42 = clip.row3.z; frustum43 = clip.row4.z; #else frustum40 = clip.row1.w - clip.row1.z; frustum41 = clip.row2.w - clip.row2.z; frustum42 = clip.row3.w - clip.row3.z; frustum43 = clip.row4.w - clip.row4.z; #endif FrustumCulling_Normalise(&frustum40, &frustum41, &frustum42, &frustum43); }