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-rw-r--r--dev/MinGfx/src/matrix4.cc890
1 files changed, 445 insertions, 445 deletions
diff --git a/dev/MinGfx/src/matrix4.cc b/dev/MinGfx/src/matrix4.cc
index e38909c..c0edde1 100644
--- a/dev/MinGfx/src/matrix4.cc
+++ b/dev/MinGfx/src/matrix4.cc
@@ -1,445 +1,445 @@
-/*
- Copyright (c) 2017,2018 Regents of the University of Minnesota.
- All Rights Reserved.
- See corresponding header file for details.
- */
-
-#include "matrix4.h"
-
-#include "gfxmath.h"
-#include <string.h>
-
-namespace mingfx {
-
-
-Matrix4::Matrix4() {
- m[0] = m[5] = m[10] = m[15] = 1.0;
- m[1] = m[2] = m[3] = m[4] = 0.0;
- m[6] = m[7] = m[8] = m[9] = 0.0;
- m[11]= m[12] = m[13] = m[14] = 0.0;
-}
-
-
-Matrix4::Matrix4(const float* a) {
- memcpy(m,a,16*sizeof(float));
-}
-
-Matrix4::Matrix4(const std::vector<float> &a) {
- for (int i=0;i<16;i++) {
- m[i] = a[i];
- }
-}
-
-Matrix4::Matrix4(const Matrix4& m2) {
- memcpy(m,m2.m,16*sizeof(float));
-}
-
-Matrix4::~Matrix4() {
-}
-
-
-bool Matrix4::operator==(const Matrix4& m2) const {
- for (int i=0;i<16;i++) {
- if (fabs(m2.m[i] - m[i]) > MINGFX_MATH_EPSILON) {
- return false;
- }
- }
- return true;
-}
-
-bool Matrix4::operator!=(const Matrix4& m2) const {
- return !(*this == m2);
-}
-
-Matrix4& Matrix4::operator=(const Matrix4& m2) {
- memcpy(m,m2.m,16*sizeof(float));
- return *this;
-}
-
-const float * Matrix4::value_ptr() const {
- return m;
-}
-
-float Matrix4::operator[](const int i) const {
- return m[i];
-}
-
-float& Matrix4::operator[](const int i) {
- return m[i];
-}
-
-float Matrix4::operator()(const int r, const int c) const {
- return m[c*4+r];
-}
-
-float& Matrix4::operator()(const int r, const int c) {
- return m[c*4+r];
-}
-
-std::vector<float> Matrix4::ToVector() const {
- std::vector<float> v;
- for (int i=0;i<16;i++) {
- v.push_back(m[i]);
- }
- return v;
-}
-
-
-
-Matrix4 Matrix4::Scale(const Vector3& v) {
- return Matrix4::FromRowMajorElements(
- v[0], 0, 0, 0,
- 0, v[1], 0, 0,
- 0, 0, v[2], 0,
- 0, 0, 0, 1
- );
-}
-
-
-Matrix4 Matrix4::Translation(const Vector3& v) {
- return Matrix4::FromRowMajorElements(
- 1, 0, 0, v[0],
- 0, 1, 0, v[1],
- 0, 0, 1, v[2],
- 0, 0, 0, 1
- );
-}
-
-
-Matrix4 Matrix4::RotationX(const float radians) {
- const float cosTheta = cos(radians);
- const float sinTheta = sin(radians);
- return Matrix4::FromRowMajorElements(
- 1, 0, 0, 0,
- 0, cosTheta, -sinTheta, 0,
- 0, sinTheta, cosTheta, 0,
- 0, 0, 0, 1
- );
-}
-
-
-Matrix4 Matrix4::RotationY(const float radians) {
- const float cosTheta = cos(radians);
- const float sinTheta = sin(radians);
- return Matrix4::FromRowMajorElements(
- cosTheta, 0, sinTheta, 0,
- 0, 1, 0, 0,
- -sinTheta, 0, cosTheta, 0,
- 0, 0, 0, 1
- );
-}
-
-
-Matrix4 Matrix4::RotationZ(const float radians) {
- const float cosTheta = cos(radians);
- const float sinTheta = sin(radians);
- return Matrix4::FromRowMajorElements(
- cosTheta, -sinTheta, 0, 0,
- sinTheta, cosTheta, 0, 0,
- 0, 0, 1, 0,
- 0, 0, 0, 1
- );
-}
-
-
-Matrix4 Matrix4::Rotation(const Point3& p, const Vector3& v, const float a) {
- const float vZ = v[2];
- const float vX = v[0];
- const float theta = atan2(vZ, vX);
- const float phi = -atan2((float)v[1], (float)sqrt(vX * vX + vZ * vZ));
-
- const Matrix4 transToOrigin = Matrix4::Translation(-1.0*Vector3(p[0], p[1], p[2]));
- const Matrix4 A = Matrix4::RotationY(theta);
- const Matrix4 B = Matrix4::RotationZ(phi);
- const Matrix4 C = Matrix4::RotationX(a);
- const Matrix4 invA = Matrix4::RotationY(-theta);
- const Matrix4 invB = Matrix4::RotationZ(-phi);
- const Matrix4 transBack = Matrix4::Translation(Vector3(p[0], p[1], p[2]));
-
- return transBack * invA * invB * C * B * A * transToOrigin;
-}
-
-
-Matrix4 Matrix4::Align(const Point3 &a_p, const Vector3 &a_v1, const Vector3 &a_v2,
- const Point3 &b_p, const Vector3 &b_v1, const Vector3 &b_v2)
-{
- Vector3 ax = a_v1.ToUnit();
- Vector3 ay = a_v2.ToUnit();
- Vector3 az = ax.Cross(ay).ToUnit();
- ay = az.Cross(ax);
- Matrix4 A = Matrix4::FromRowMajorElements(ax[0], ay[0], az[0], a_p[0],
- ax[1], ay[1], az[1], a_p[1],
- ax[2], ay[2], az[2], a_p[2],
- 0, 0, 0, 1);
-
- Vector3 bx = b_v1.ToUnit();
- Vector3 by = b_v2.ToUnit();
- Vector3 bz = bx.Cross(by).ToUnit();
- by = bz.Cross(bx);
- Matrix4 B = Matrix4::FromRowMajorElements(bx[0], by[0], bz[0], b_p[0],
- bx[1], by[1], bz[1], b_p[1],
- bx[2], by[2], bz[2], b_p[2],
- 0, 0, 0, 1);
- return B * A.Inverse();
-}
-
-
-
-Matrix4 Matrix4::LookAt(Point3 eye, Point3 target, Vector3 up) {
- Vector3 lookDir = (target - eye).ToUnit();
-
- // desired x,y,z for the camera itself
- Vector3 z = -lookDir;
- Vector3 x = up.Cross(z).ToUnit();
- Vector3 y = z.Cross(x);
-
- // for the view matrix rotation, we want the inverse of the rotation for the
- // camera, and the inverse of a rotation matrix is its transpose, so the
- // x,y,z colums become x,y,z rows.
- Matrix4 R = Matrix4::FromRowMajorElements(
- x[0], x[1], x[2], 0,
- y[0], y[1], y[2], 0,
- z[0], z[1], z[2], 0,
- 0, 0, 0, 1
- );
-
- // also need to translate by -eye
- Matrix4 T = Matrix4::Translation(Point3(0,0,0) - eye);
-
- return R * T;
-}
-
-Matrix4 Matrix4::Perspective(float fovyInDegrees, float aspectRatio,
- float nearVal, float farVal)
-{
- // https://www.khronos.org/opengl/wiki/GluPerspective_code
- float ymax, xmax;
- ymax = nearVal * tanf(fovyInDegrees * GfxMath::PI / 360.0f);
- // ymin = -ymax;
- // xmin = -ymax * aspectRatio;
- xmax = ymax * aspectRatio;
- return Matrix4::Frustum(-xmax, xmax, -ymax, ymax, nearVal, farVal);
-}
-
-
-Matrix4 Matrix4::Frustum(float left, float right,
- float bottom, float top,
- float nearVal, float farVal)
-{
- return Matrix4::FromRowMajorElements(
- 2.0f*nearVal/(right-left), 0.0f, (right+left)/(right-left), 0.0f,
- 0.0f, 2.0f*nearVal/(top-bottom), (top+bottom)/(top-bottom), 0.0f,
- 0.0f, 0.0f, -(farVal+nearVal)/(farVal-nearVal), -2.0f*farVal*nearVal/(farVal-nearVal),
- 0.0f, 0.0f, -1.0f, 0.0
- );
-}
-
-
-Matrix4 Matrix4::FromRowMajorElements(
- const float r1c1, const float r1c2, const float r1c3, const float r1c4,
- const float r2c1, const float r2c2, const float r2c3, const float r2c4,
- const float r3c1, const float r3c2, const float r3c3, const float r3c4,
- const float r4c1, const float r4c2, const float r4c3, const float r4c4)
-{
- float m[16];
- m[0]=r1c1; m[4]=r1c2; m[8]=r1c3; m[12]=r1c4;
- m[1]=r2c1; m[5]=r2c2; m[9]=r2c3; m[13]=r2c4;
- m[2]=r3c1; m[6]=r3c2; m[10]=r3c3; m[14]=r3c4;
- m[3]=r4c1; m[7]=r4c2; m[11]=r4c3; m[15]=r4c4;
- return Matrix4(m);
-}
-
-
-
-
-Matrix4 Matrix4::Orthonormal() const {
- Vector3 x = ColumnToVector3(0).ToUnit();
- Vector3 y = ColumnToVector3(1);
- y = (y - y.Dot(x)*x).ToUnit();
- Vector3 z = x.Cross(y).ToUnit();
- return Matrix4::FromRowMajorElements(
- x[0], y[0], z[0], m[12],
- x[1], y[1], z[1], m[13],
- x[2], y[2], z[2], m[14],
- m[3], m[7], m[11], m[15]
- );
-}
-
-
-Matrix4 Matrix4::Transpose() const {
- return Matrix4::FromRowMajorElements(
- m[0], m[1], m[2], m[3],
- m[4], m[5], m[6], m[7],
- m[8], m[9], m[10], m[11],
- m[12], m[13], m[14], m[15]
- );
-}
-
-
-
-
-// Returns the determinant of the 3x3 matrix formed by excluding the specified row and column
-// from the 4x4 matrix. The formula for the determinant of a 3x3 is discussed on
-// page 705 of Hill & Kelley, but note that there is a typo within the m_ij indices in the
-// equation in the book that corresponds to the cofactor02 line in the code below.
-float Matrix4::SubDeterminant(int excludeRow, int excludeCol) const {
- // Compute non-excluded row and column indices
- int row[3];
- int col[3];
-
- int r=0;
- int c=0;
- for (int i=0; i<4; i++) {
- if (i != excludeRow) {
- row[r] = i;
- r++;
- }
- if (i != excludeCol) {
- col[c] = i;
- c++;
- }
- }
-
- // Compute the cofactors of each element in the first row
- float cofactor00 = (*this)(row[1],col[1]) * (*this)(row[2],col[2]) - (*this)(row[1],col[2]) * (*this)(row[2],col[1]);
- float cofactor01 = - ((*this)(row[1],col[0]) * (*this)(row[2],col[2]) - (*this)(row[1],col[2]) * (*this)(row[2],col[0]));
- float cofactor02 = (*this)(row[1],col[0]) * (*this)(row[2],col[1]) - (*this)(row[1],col[1]) * (*this)(row[2],col[0]);
-
- // The determinant is then the dot product of the first row and the cofactors of the first row
- return (*this)(row[0],col[0])*cofactor00 + (*this)(row[0],col[1])*cofactor01 + (*this)(row[0],col[2])*cofactor02;
-}
-
-// Returns the cofactor matrix. The cofactor matrix is a matrix where each element c_ij is the cofactor
-// of the corresponding element m_ij in M. The cofactor of each element m_ij is defined as (-1)^(i+j) times
-// the determinant of the "submatrix" formed by deleting the i-th row and j-th column from M.
-// See the definition in section A2.1.4 (page 705) in Hill & Kelley.
-Matrix4 Matrix4::Cofactor() const {
- Matrix4 out;
- // We'll use i to incrementally compute -1^(r+c)
- int i = 1;
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- // Compute the determinant of the 3x3 submatrix
- float det = SubDeterminant(r, c);
- out(r,c) = i * det;
- i = -i;
- }
- i = -i;
- }
- return out;
-}
-
-// Returns the determinant of the 4x4 matrix
-// See the hint in step 2 in Appendix A2.1.5 (page 706) in Hill & Kelley to learn how to compute this
-float Matrix4::Determinant() const {
- // The determinant is the dot product of any row of C (the cofactor matrix of m) with the corresponding row of m
- Matrix4 C = Cofactor();
- return C(0,0)*(*this)(0,0) + C(0,1)*(*this)(0,1) + C(0,2)*(*this)(0,2) + C(0,3)*(*this)(0,3);
-}
-
-// Returns the inverse of the 4x4 matrix if it is nonsingular. If it is singular, then returns the
-// identity matrix.
-Matrix4 Matrix4::Inverse() const {
- // Check for singular matrix
- float det = Determinant();
- if (fabs(det) < 1e-8) {
- return Matrix4();
- }
-
- // m in nonsingular, so compute inverse using the 4-step procedure outlined in Appendix A2.1.5
- // (page 706) in Hill & Kelley
- // 1. Find cofactor matrix C
- Matrix4 C = Cofactor();
- // 2. Find the determinant of M as the dot prod of any row of C with the corresponding row of M.
- // det = determinant(m);
- // 3. Transpose C to get Ctrans
- Matrix4 Ctrans = C.Transpose();
- // 4. Scale each element of Ctrans by (1/det)
- return Ctrans * (1.0f / det);
-}
-
-
-Vector3 Matrix4::ColumnToVector3(int c) const {
- return Vector3(m[c*4], m[c*4+1], m[c*4+2]);
-}
-
-Point3 Matrix4::ColumnToPoint3(int c) const {
- return Point3(m[c*4], m[c*4+1], m[c*4+2]);
-}
-
-
-
-
-Matrix4 operator*(const Matrix4& m, const float& s) {
- Matrix4 result;
- for (int r = 0; r < 4; r++) {
- for (int c = 0; c < 4; c++) {
- result(r,c) = m(r,c) * s;
- }
- }
- return result;
-}
-
-Matrix4 operator*(const float& s, const Matrix4& m) {
- return m*s;
-}
-
-
-Point3 operator*(const Matrix4& m, const Point3& p) {
- // For our points, p[3]=1 and we don't even bother storing p[3], so need to homogenize
- // by dividing by w before returning the new point.
- const float winv = 1.0f / (p[0] * m(3,0) + p[1] * m(3,1) + p[2] * m(3,2) + 1.0f * m(3,3));
- return Point3(winv * (p[0] * m(0,0) + p[1] * m(0,1) + p[2] * m(0,2) + 1.0f * m(0,3)),
- winv * (p[0] * m(1,0) + p[1] * m(1,1) + p[2] * m(1,2) + 1.0f * m(1,3)),
- winv * (p[0] * m(2,0) + p[1] * m(2,1) + p[2] * m(2,2) + 1.0f * m(2,3)));
-
-}
-
-
-Vector3 operator*(const Matrix4& m, const Vector3& v) {
- // For a vector v[3]=0
- return Vector3(v[0] * m(0,0) + v[1] * m(0,1) + v[2] * m(0,2),
- v[0] * m(1,0) + v[1] * m(1,1) + v[2] * m(1,2),
- v[0] * m(2,0) + v[1] * m(2,1) + v[2] * m(2,2));
-
-}
-
-
-
-Matrix4 operator*(const Matrix4& m1, const Matrix4& m2) {
- Matrix4 m = Matrix4::FromRowMajorElements(0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0);
- for (int r = 0; r < 4; r++) {
- for (int c = 0; c < 4; c++) {
- for (int i = 0; i < 4; i++) {
- m(r,c) += m1(r,i) * m2(i,c);
- }
- }
- }
- return m;
-}
-
-Ray operator*(const Matrix4& m, const Ray& r) {
- Point3 p = m * r.origin();
- Vector3 d = m * r.direction();
- return Ray(p, d);
-}
-
-
-std::ostream & operator<< ( std::ostream &os, const Matrix4 &m) {
- // format: [[r1c1, r1c2, r1c3, r1c4], [r2c1, r2c2, r2c3, r2c4], etc.. ]
- return os << "[[" << m(0,0) << ", " << m(0,1) << ", " << m(0,2) << ", " << m(0,3) << "], "
- << "[" << m(1,0) << ", " << m(1,1) << ", " << m(1,2) << ", " << m(1,3) << "], "
- << "[" << m(2,0) << ", " << m(2,1) << ", " << m(2,2) << ", " << m(2,3) << "], "
- << "[" << m(3,0) << ", " << m(3,1) << ", " << m(3,2) << ", " << m(3,3) << "]]";
-}
-
-std::istream & operator>> ( std::istream &is, Matrix4 &m) {
- // format: [[r1c1, r1c2, r1c3, r1c4], [r2c1, r2c2, r2c3, r2c4], etc.. ]
- char c;
- return is >> c >> c >> m(0,0) >> c >> m(0,1) >> c >> m(0,2) >> c >> m(0,3) >> c >> c
- >> c >> m(1,0) >> c >> m(1,1) >> c >> m(1,2) >> c >> m(1,3) >> c >> c
- >> c >> m(2,0) >> c >> m(2,1) >> c >> m(2,2) >> c >> m(2,3) >> c >> c
- >> c >> m(3,0) >> c >> m(3,1) >> c >> m(3,2) >> c >> m(3,3) >> c >> c;
-}
-
-} // end namespace
+/*
+ Copyright (c) 2017,2018 Regents of the University of Minnesota.
+ All Rights Reserved.
+ See corresponding header file for details.
+ */
+
+#include "matrix4.h"
+
+#include "gfxmath.h"
+#include <string.h>
+
+namespace mingfx {
+
+
+Matrix4::Matrix4() {
+ m[0] = m[5] = m[10] = m[15] = 1.0;
+ m[1] = m[2] = m[3] = m[4] = 0.0;
+ m[6] = m[7] = m[8] = m[9] = 0.0;
+ m[11]= m[12] = m[13] = m[14] = 0.0;
+}
+
+
+Matrix4::Matrix4(const float* a) {
+ memcpy(m,a,16*sizeof(float));
+}
+
+Matrix4::Matrix4(const std::vector<float> &a) {
+ for (int i=0;i<16;i++) {
+ m[i] = a[i];
+ }
+}
+
+Matrix4::Matrix4(const Matrix4& m2) {
+ memcpy(m,m2.m,16*sizeof(float));
+}
+
+Matrix4::~Matrix4() {
+}
+
+
+bool Matrix4::operator==(const Matrix4& m2) const {
+ for (int i=0;i<16;i++) {
+ if (fabs(m2.m[i] - m[i]) > MINGFX_MATH_EPSILON) {
+ return false;
+ }
+ }
+ return true;
+}
+
+bool Matrix4::operator!=(const Matrix4& m2) const {
+ return !(*this == m2);
+}
+
+Matrix4& Matrix4::operator=(const Matrix4& m2) {
+ memcpy(m,m2.m,16*sizeof(float));
+ return *this;
+}
+
+const float * Matrix4::value_ptr() const {
+ return m;
+}
+
+float Matrix4::operator[](const int i) const {
+ return m[i];
+}
+
+float& Matrix4::operator[](const int i) {
+ return m[i];
+}
+
+float Matrix4::operator()(const int r, const int c) const {
+ return m[c*4+r];
+}
+
+float& Matrix4::operator()(const int r, const int c) {
+ return m[c*4+r];
+}
+
+std::vector<float> Matrix4::ToVector() const {
+ std::vector<float> v;
+ for (int i=0;i<16;i++) {
+ v.push_back(m[i]);
+ }
+ return v;
+}
+
+
+
+Matrix4 Matrix4::Scale(const Vector3& v) {
+ return Matrix4::FromRowMajorElements(
+ v[0], 0, 0, 0,
+ 0, v[1], 0, 0,
+ 0, 0, v[2], 0,
+ 0, 0, 0, 1
+ );
+}
+
+
+Matrix4 Matrix4::Translation(const Vector3& v) {
+ return Matrix4::FromRowMajorElements(
+ 1, 0, 0, v[0],
+ 0, 1, 0, v[1],
+ 0, 0, 1, v[2],
+ 0, 0, 0, 1
+ );
+}
+
+
+Matrix4 Matrix4::RotationX(const float radians) {
+ const float cosTheta = cos(radians);
+ const float sinTheta = sin(radians);
+ return Matrix4::FromRowMajorElements(
+ 1, 0, 0, 0,
+ 0, cosTheta, -sinTheta, 0,
+ 0, sinTheta, cosTheta, 0,
+ 0, 0, 0, 1
+ );
+}
+
+
+Matrix4 Matrix4::RotationY(const float radians) {
+ const float cosTheta = cos(radians);
+ const float sinTheta = sin(radians);
+ return Matrix4::FromRowMajorElements(
+ cosTheta, 0, sinTheta, 0,
+ 0, 1, 0, 0,
+ -sinTheta, 0, cosTheta, 0,
+ 0, 0, 0, 1
+ );
+}
+
+
+Matrix4 Matrix4::RotationZ(const float radians) {
+ const float cosTheta = cos(radians);
+ const float sinTheta = sin(radians);
+ return Matrix4::FromRowMajorElements(
+ cosTheta, -sinTheta, 0, 0,
+ sinTheta, cosTheta, 0, 0,
+ 0, 0, 1, 0,
+ 0, 0, 0, 1
+ );
+}
+
+
+Matrix4 Matrix4::Rotation(const Point3& p, const Vector3& v, const float a) {
+ const float vZ = v[2];
+ const float vX = v[0];
+ const float theta = atan2(vZ, vX);
+ const float phi = -atan2((float)v[1], (float)sqrt(vX * vX + vZ * vZ));
+
+ const Matrix4 transToOrigin = Matrix4::Translation(-1.0*Vector3(p[0], p[1], p[2]));
+ const Matrix4 A = Matrix4::RotationY(theta);
+ const Matrix4 B = Matrix4::RotationZ(phi);
+ const Matrix4 C = Matrix4::RotationX(a);
+ const Matrix4 invA = Matrix4::RotationY(-theta);
+ const Matrix4 invB = Matrix4::RotationZ(-phi);
+ const Matrix4 transBack = Matrix4::Translation(Vector3(p[0], p[1], p[2]));
+
+ return transBack * invA * invB * C * B * A * transToOrigin;
+}
+
+
+Matrix4 Matrix4::Align(const Point3 &a_p, const Vector3 &a_v1, const Vector3 &a_v2,
+ const Point3 &b_p, const Vector3 &b_v1, const Vector3 &b_v2)
+{
+ Vector3 ax = a_v1.ToUnit();
+ Vector3 ay = a_v2.ToUnit();
+ Vector3 az = ax.Cross(ay).ToUnit();
+ ay = az.Cross(ax);
+ Matrix4 A = Matrix4::FromRowMajorElements(ax[0], ay[0], az[0], a_p[0],
+ ax[1], ay[1], az[1], a_p[1],
+ ax[2], ay[2], az[2], a_p[2],
+ 0, 0, 0, 1);
+
+ Vector3 bx = b_v1.ToUnit();
+ Vector3 by = b_v2.ToUnit();
+ Vector3 bz = bx.Cross(by).ToUnit();
+ by = bz.Cross(bx);
+ Matrix4 B = Matrix4::FromRowMajorElements(bx[0], by[0], bz[0], b_p[0],
+ bx[1], by[1], bz[1], b_p[1],
+ bx[2], by[2], bz[2], b_p[2],
+ 0, 0, 0, 1);
+ return B * A.Inverse();
+}
+
+
+
+Matrix4 Matrix4::LookAt(Point3 eye, Point3 target, Vector3 up) {
+ Vector3 lookDir = (target - eye).ToUnit();
+
+ // desired x,y,z for the camera itself
+ Vector3 z = -lookDir;
+ Vector3 x = up.Cross(z).ToUnit();
+ Vector3 y = z.Cross(x);
+
+ // for the view matrix rotation, we want the inverse of the rotation for the
+ // camera, and the inverse of a rotation matrix is its transpose, so the
+ // x,y,z colums become x,y,z rows.
+ Matrix4 R = Matrix4::FromRowMajorElements(
+ x[0], x[1], x[2], 0,
+ y[0], y[1], y[2], 0,
+ z[0], z[1], z[2], 0,
+ 0, 0, 0, 1
+ );
+
+ // also need to translate by -eye
+ Matrix4 T = Matrix4::Translation(Point3(0,0,0) - eye);
+
+ return R * T;
+}
+
+Matrix4 Matrix4::Perspective(float fovyInDegrees, float aspectRatio,
+ float nearVal, float farVal)
+{
+ // https://www.khronos.org/opengl/wiki/GluPerspective_code
+ float ymax, xmax;
+ ymax = nearVal * tanf(fovyInDegrees * GfxMath::PI / 360.0f);
+ // ymin = -ymax;
+ // xmin = -ymax * aspectRatio;
+ xmax = ymax * aspectRatio;
+ return Matrix4::Frustum(-xmax, xmax, -ymax, ymax, nearVal, farVal);
+}
+
+
+Matrix4 Matrix4::Frustum(float left, float right,
+ float bottom, float top,
+ float nearVal, float farVal)
+{
+ return Matrix4::FromRowMajorElements(
+ 2.0f*nearVal/(right-left), 0.0f, (right+left)/(right-left), 0.0f,
+ 0.0f, 2.0f*nearVal/(top-bottom), (top+bottom)/(top-bottom), 0.0f,
+ 0.0f, 0.0f, -(farVal+nearVal)/(farVal-nearVal), -2.0f*farVal*nearVal/(farVal-nearVal),
+ 0.0f, 0.0f, -1.0f, 0.0
+ );
+}
+
+
+Matrix4 Matrix4::FromRowMajorElements(
+ const float r1c1, const float r1c2, const float r1c3, const float r1c4,
+ const float r2c1, const float r2c2, const float r2c3, const float r2c4,
+ const float r3c1, const float r3c2, const float r3c3, const float r3c4,
+ const float r4c1, const float r4c2, const float r4c3, const float r4c4)
+{
+ float m[16];
+ m[0]=r1c1; m[4]=r1c2; m[8]=r1c3; m[12]=r1c4;
+ m[1]=r2c1; m[5]=r2c2; m[9]=r2c3; m[13]=r2c4;
+ m[2]=r3c1; m[6]=r3c2; m[10]=r3c3; m[14]=r3c4;
+ m[3]=r4c1; m[7]=r4c2; m[11]=r4c3; m[15]=r4c4;
+ return Matrix4(m);
+}
+
+
+
+
+Matrix4 Matrix4::Orthonormal() const {
+ Vector3 x = ColumnToVector3(0).ToUnit();
+ Vector3 y = ColumnToVector3(1);
+ y = (y - y.Dot(x)*x).ToUnit();
+ Vector3 z = x.Cross(y).ToUnit();
+ return Matrix4::FromRowMajorElements(
+ x[0], y[0], z[0], m[12],
+ x[1], y[1], z[1], m[13],
+ x[2], y[2], z[2], m[14],
+ m[3], m[7], m[11], m[15]
+ );
+}
+
+
+Matrix4 Matrix4::Transpose() const {
+ return Matrix4::FromRowMajorElements(
+ m[0], m[1], m[2], m[3],
+ m[4], m[5], m[6], m[7],
+ m[8], m[9], m[10], m[11],
+ m[12], m[13], m[14], m[15]
+ );
+}
+
+
+
+
+// Returns the determinant of the 3x3 matrix formed by excluding the specified row and column
+// from the 4x4 matrix. The formula for the determinant of a 3x3 is discussed on
+// page 705 of Hill & Kelley, but note that there is a typo within the m_ij indices in the
+// equation in the book that corresponds to the cofactor02 line in the code below.
+float Matrix4::SubDeterminant(int excludeRow, int excludeCol) const {
+ // Compute non-excluded row and column indices
+ int row[3];
+ int col[3];
+
+ int r=0;
+ int c=0;
+ for (int i=0; i<4; i++) {
+ if (i != excludeRow) {
+ row[r] = i;
+ r++;
+ }
+ if (i != excludeCol) {
+ col[c] = i;
+ c++;
+ }
+ }
+
+ // Compute the cofactors of each element in the first row
+ float cofactor00 = (*this)(row[1],col[1]) * (*this)(row[2],col[2]) - (*this)(row[1],col[2]) * (*this)(row[2],col[1]);
+ float cofactor01 = - ((*this)(row[1],col[0]) * (*this)(row[2],col[2]) - (*this)(row[1],col[2]) * (*this)(row[2],col[0]));
+ float cofactor02 = (*this)(row[1],col[0]) * (*this)(row[2],col[1]) - (*this)(row[1],col[1]) * (*this)(row[2],col[0]);
+
+ // The determinant is then the dot product of the first row and the cofactors of the first row
+ return (*this)(row[0],col[0])*cofactor00 + (*this)(row[0],col[1])*cofactor01 + (*this)(row[0],col[2])*cofactor02;
+}
+
+// Returns the cofactor matrix. The cofactor matrix is a matrix where each element c_ij is the cofactor
+// of the corresponding element m_ij in M. The cofactor of each element m_ij is defined as (-1)^(i+j) times
+// the determinant of the "submatrix" formed by deleting the i-th row and j-th column from M.
+// See the definition in section A2.1.4 (page 705) in Hill & Kelley.
+Matrix4 Matrix4::Cofactor() const {
+ Matrix4 out;
+ // We'll use i to incrementally compute -1^(r+c)
+ int i = 1;
+ for (int r = 0; r < 4; ++r) {
+ for (int c = 0; c < 4; ++c) {
+ // Compute the determinant of the 3x3 submatrix
+ float det = SubDeterminant(r, c);
+ out(r,c) = i * det;
+ i = -i;
+ }
+ i = -i;
+ }
+ return out;
+}
+
+// Returns the determinant of the 4x4 matrix
+// See the hint in step 2 in Appendix A2.1.5 (page 706) in Hill & Kelley to learn how to compute this
+float Matrix4::Determinant() const {
+ // The determinant is the dot product of any row of C (the cofactor matrix of m) with the corresponding row of m
+ Matrix4 C = Cofactor();
+ return C(0,0)*(*this)(0,0) + C(0,1)*(*this)(0,1) + C(0,2)*(*this)(0,2) + C(0,3)*(*this)(0,3);
+}
+
+// Returns the inverse of the 4x4 matrix if it is nonsingular. If it is singular, then returns the
+// identity matrix.
+Matrix4 Matrix4::Inverse() const {
+ // Check for singular matrix
+ float det = Determinant();
+ if (fabs(det) < 1e-8) {
+ return Matrix4();
+ }
+
+ // m in nonsingular, so compute inverse using the 4-step procedure outlined in Appendix A2.1.5
+ // (page 706) in Hill & Kelley
+ // 1. Find cofactor matrix C
+ Matrix4 C = Cofactor();
+ // 2. Find the determinant of M as the dot prod of any row of C with the corresponding row of M.
+ // det = determinant(m);
+ // 3. Transpose C to get Ctrans
+ Matrix4 Ctrans = C.Transpose();
+ // 4. Scale each element of Ctrans by (1/det)
+ return Ctrans * (1.0f / det);
+}
+
+
+Vector3 Matrix4::ColumnToVector3(int c) const {
+ return Vector3(m[c*4], m[c*4+1], m[c*4+2]);
+}
+
+Point3 Matrix4::ColumnToPoint3(int c) const {
+ return Point3(m[c*4], m[c*4+1], m[c*4+2]);
+}
+
+
+
+
+Matrix4 operator*(const Matrix4& m, const float& s) {
+ Matrix4 result;
+ for (int r = 0; r < 4; r++) {
+ for (int c = 0; c < 4; c++) {
+ result(r,c) = m(r,c) * s;
+ }
+ }
+ return result;
+}
+
+Matrix4 operator*(const float& s, const Matrix4& m) {
+ return m*s;
+}
+
+
+Point3 operator*(const Matrix4& m, const Point3& p) {
+ // For our points, p[3]=1 and we don't even bother storing p[3], so need to homogenize
+ // by dividing by w before returning the new point.
+ const float winv = 1.0f / (p[0] * m(3,0) + p[1] * m(3,1) + p[2] * m(3,2) + 1.0f * m(3,3));
+ return Point3(winv * (p[0] * m(0,0) + p[1] * m(0,1) + p[2] * m(0,2) + 1.0f * m(0,3)),
+ winv * (p[0] * m(1,0) + p[1] * m(1,1) + p[2] * m(1,2) + 1.0f * m(1,3)),
+ winv * (p[0] * m(2,0) + p[1] * m(2,1) + p[2] * m(2,2) + 1.0f * m(2,3)));
+
+}
+
+
+Vector3 operator*(const Matrix4& m, const Vector3& v) {
+ // For a vector v[3]=0
+ return Vector3(v[0] * m(0,0) + v[1] * m(0,1) + v[2] * m(0,2),
+ v[0] * m(1,0) + v[1] * m(1,1) + v[2] * m(1,2),
+ v[0] * m(2,0) + v[1] * m(2,1) + v[2] * m(2,2));
+
+}
+
+
+
+Matrix4 operator*(const Matrix4& m1, const Matrix4& m2) {
+ Matrix4 m = Matrix4::FromRowMajorElements(0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0);
+ for (int r = 0; r < 4; r++) {
+ for (int c = 0; c < 4; c++) {
+ for (int i = 0; i < 4; i++) {
+ m(r,c) += m1(r,i) * m2(i,c);
+ }
+ }
+ }
+ return m;
+}
+
+Ray operator*(const Matrix4& m, const Ray& r) {
+ Point3 p = m * r.origin();
+ Vector3 d = m * r.direction();
+ return Ray(p, d);
+}
+
+
+std::ostream & operator<< ( std::ostream &os, const Matrix4 &m) {
+ // format: [[r1c1, r1c2, r1c3, r1c4], [r2c1, r2c2, r2c3, r2c4], etc.. ]
+ return os << "[[" << m(0,0) << ", " << m(0,1) << ", " << m(0,2) << ", " << m(0,3) << "], "
+ << "[" << m(1,0) << ", " << m(1,1) << ", " << m(1,2) << ", " << m(1,3) << "], "
+ << "[" << m(2,0) << ", " << m(2,1) << ", " << m(2,2) << ", " << m(2,3) << "], "
+ << "[" << m(3,0) << ", " << m(3,1) << ", " << m(3,2) << ", " << m(3,3) << "]]";
+}
+
+std::istream & operator>> ( std::istream &is, Matrix4 &m) {
+ // format: [[r1c1, r1c2, r1c3, r1c4], [r2c1, r2c2, r2c3, r2c4], etc.. ]
+ char c;
+ return is >> c >> c >> m(0,0) >> c >> m(0,1) >> c >> m(0,2) >> c >> m(0,3) >> c >> c
+ >> c >> m(1,0) >> c >> m(1,1) >> c >> m(1,2) >> c >> m(1,3) >> c >> c
+ >> c >> m(2,0) >> c >> m(2,1) >> c >> m(2,2) >> c >> m(2,3) >> c >> c
+ >> c >> m(3,0) >> c >> m(3,1) >> c >> m(3,2) >> c >> m(3,3) >> c >> c;
+}
+
+} // end namespace
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