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-/**
- @file Matrix4.cpp
-
-
- @maintainer Morgan McGuire, matrix@graphics3d.com
-
- @created 2003-10-02
- @edited 2008-07-17
- */
-
-#include "G3D/platform.h"
-#include "G3D/Matrix4.h"
-#include "G3D/Matrix3.h"
-#include "G3D/Vector4.h"
-#include "G3D/Vector3.h"
-#include "G3D/BinaryInput.h"
-#include "G3D/BinaryOutput.h"
-#include "G3D/CoordinateFrame.h"
-#include "G3D/Rect2D.h"
-
-namespace G3D {
-
-const Matrix4& Matrix4::identity() {
- static Matrix4 m(
- 1, 0, 0, 0,
- 0, 1, 0, 0,
- 0, 0, 1, 0,
- 0, 0, 0, 1);
- return m;
-}
-
-
-const Matrix4& Matrix4::zero() {
- static Matrix4 m(
- 0, 0, 0, 0,
- 0, 0, 0, 0,
- 0, 0, 0, 0,
- 0, 0, 0, 0);
- return m;
-}
-
-
-Matrix4::Matrix4(const class CoordinateFrame& cframe) {
- for (int r = 0; r < 3; ++r) {
- for (int c = 0; c < 3; ++c) {
- elt[r][c] = cframe.rotation[r][c];
- }
- elt[r][3] = cframe.translation[r];
- }
- elt[3][0] = 0.0f;
- elt[3][1] = 0.0f;
- elt[3][2] = 0.0f;
- elt[3][3] = 1.0f;
-}
-
-Matrix4::Matrix4(const Matrix3& upper3x3, const Vector3& lastCol) {
- for (int r = 0; r < 3; ++r) {
- for (int c = 0; c < 3; ++c) {
- elt[r][c] = upper3x3[r][c];
- }
- elt[r][3] = lastCol[r];
- }
- elt[3][0] = 0.0f;
- elt[3][1] = 0.0f;
- elt[3][2] = 0.0f;
- elt[3][3] = 1.0f;
-}
-
-
-Matrix3 Matrix4::upper3x3() const {
- return Matrix3(elt[0][0], elt[0][1], elt[0][2],
- elt[1][0], elt[1][1], elt[1][2],
- elt[2][0], elt[2][1], elt[2][2]);
-}
-
-
-Matrix4 Matrix4::orthogonalProjection(
- const class Rect2D& rect,
- float nearval,
- float farval) {
- return Matrix4::orthogonalProjection(rect.x0(), rect.x1(), rect.y1(), rect.y0(), nearval, farval);
-}
-
-
-Matrix4 Matrix4::orthogonalProjection(
- float left,
- float right,
- float bottom,
- float top,
- float nearval,
- float farval) {
-
- // Adapted from Mesa. Note that Microsoft (http://msdn.microsoft.com/library/default.asp?url=/library/en-us/opengl/glfunc03_8qnj.asp)
- // and Linux (http://www.xfree86.org/current/glOrtho.3.html) have different matrices shown in their documentation.
-
- float x, y, z;
- float tx, ty, tz;
-
- x = 2.0f / (right-left);
- y = 2.0f / (top-bottom);
- z = -2.0f / (farval-nearval);
- tx = -(right+left) / (right-left);
- ty = -(top+bottom) / (top-bottom);
- tz = -(farval+nearval) / (farval-nearval);
-
- return
- Matrix4( x , 0.0f, 0.0f, tx,
- 0.0f, y , 0.0f, ty,
- 0.0f, 0.0f, z , tz,
- 0.0f, 0.0f, 0.0f, 1.0f);
-}
-
-
-Matrix4 Matrix4::perspectiveProjection(
- float left,
- float right,
- float bottom,
- float top,
- float nearval,
- float farval) {
-
- float x, y, a, b, c, d;
-
- x = (2.0f*nearval) / (right-left);
- y = (2.0f*nearval) / (top-bottom);
- a = (right+left) / (right-left);
- b = (top+bottom) / (top-bottom);
-
- if ((float)farval >= (float)inf()) {
- // Infinite view frustum
- c = -1.0f;
- d = -2.0f * nearval;
- } else {
- c = -(farval+nearval) / (farval-nearval);
- d = -(2.0f*farval*nearval) / (farval-nearval);
- }
-
- return Matrix4(
- x, 0, a, 0,
- 0, y, b, 0,
- 0, 0, c, d,
- 0, 0, -1, 0);
-}
-
-
-Matrix4::Matrix4(
- float r1c1, float r1c2, float r1c3, float r1c4,
- float r2c1, float r2c2, float r2c3, float r2c4,
- float r3c1, float r3c2, float r3c3, float r3c4,
- float r4c1, float r4c2, float r4c3, float r4c4) {
- elt[0][0] = r1c1; elt[0][1] = r1c2; elt[0][2] = r1c3; elt[0][3] = r1c4;
- elt[1][0] = r2c1; elt[1][1] = r2c2; elt[1][2] = r2c3; elt[1][3] = r2c4;
- elt[2][0] = r3c1; elt[2][1] = r3c2; elt[2][2] = r3c3; elt[2][3] = r3c4;
- elt[3][0] = r4c1; elt[3][1] = r4c2; elt[3][2] = r4c3; elt[3][3] = r4c4;
-}
-
-/**
- init should be <B>row major</B>.
- */
-Matrix4::Matrix4(const float* init) {
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- elt[r][c] = init[r * 4 + c];
- }
- }
-}
-
-
-Matrix4::Matrix4(const double* init) {
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- elt[r][c] = (float)init[r * 4 + c];
- }
- }
-}
-
-
-Matrix4::Matrix4() {
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- elt[r][c] = 0;
- }
- }
-}
-
-
-void Matrix4::setRow(int r, const Vector4& v) {
- for (int c = 0; c < 4; ++c) {
- elt[r][c] = v[c];
- }
-}
-
-
-void Matrix4::setColumn(int c, const Vector4& v) {
- for (int r = 0; r < 4; ++r) {
- elt[r][c] = v[r];
- }
-}
-
-
-Vector4 Matrix4::getRow(int r) const {
- return row(r);
-}
-
-
-const Vector4& Matrix4::row(int r) const {
- return reinterpret_cast<const Vector4*>(elt[r])[0];
-}
-
-
-Vector4 Matrix4::getColumn(int c) const {
- return column(c);
-}
-
-Vector4 Matrix4::column(int c) const {
- Vector4 v;
- for (int r = 0; r < 4; ++r) {
- v[r] = elt[r][c];
- }
- return v;
-}
-
-
-Matrix4 Matrix4::operator*(const Matrix4& other) const {
- Matrix4 result;
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- for (int i = 0; i < 4; ++i) {
- result.elt[r][c] += elt[r][i] * other.elt[i][c];
- }
- }
- }
-
- return result;
-}
-
-
-Matrix4 Matrix4::operator*(const float s) const {
- Matrix4 result;
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- result.elt[r][c] = elt[r][c] * s;
- }
- }
-
- return result;
-}
-
-
-Vector3 Matrix4::homoMul(const class Vector3& v, float w) const {
- Vector4 r = (*this) * Vector4(v, w);
- return r.xyz() * (1.0f / r.w);
-}
-
-
-Vector4 Matrix4::operator*(const Vector4& vector) const {
- Vector4 result(0,0,0,0);
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- result[r] += elt[r][c] * vector[c];
- }
- }
-
- return result;
-}
-
-
-Matrix4 Matrix4::transpose() const {
- Matrix4 result;
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- result.elt[c][r] = elt[r][c];
- }
- }
-
- return result;
-}
-
-
-bool Matrix4::operator!=(const Matrix4& other) const {
- return ! (*this == other);
-}
-
-
-bool Matrix4::operator==(const Matrix4& other) const {
-
- // If the bit patterns are identical, they must be
- // the same matrix. If not, they *might* still have
- // equal elements due to floating point weirdness.
- if (memcmp(this, &other, sizeof(Matrix4) == 0)) {
- return true;
- }
-
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- if (elt[r][c] != other.elt[r][c]) {
- return false;
- }
- }
- }
-
- return true;
-}
-
-
-float Matrix4::determinant() const {
- // Determinant is the dot product of the first row and the first row
- // of cofactors (i.e. the first col of the adjoint matrix)
- return cofactor().getRow(0).dot(getRow(0));
-}
-
-
-Matrix4 Matrix4::adjoint() const {
- return cofactor().transpose();
-}
-
-
-Matrix4 Matrix4::inverse() const {
- // Inverse = adjoint / determinant
-
- Matrix4 A = adjoint();
-
- // Determinant is the dot product of the first row and the first row
- // of cofactors (i.e. the first col of the adjoint matrix)
- float det = A.getColumn(0).dot(getRow(0));
-
- return A * (1.0f / det);
-}
-
-
-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.elt[r][c] = i * det;
- i = -i;
- }
- i = -i;
- }
-
- return out;
-}
-
-
-float Matrix4::subDeterminant(int excludeRow, int excludeCol) const {
- // Compute non-excluded row and column indices
- int row[3];
- int col[3];
-
- for (int i = 0; i < 3; ++i) {
- row[i] = i;
- col[i] = i;
-
- if (i >= excludeRow) {
- ++row[i];
- }
- if (i >= excludeCol) {
- ++col[i];
- }
- }
-
- // Compute the first row of cofactors
- float cofactor00 =
- elt[row[1]][col[1]] * elt[row[2]][col[2]] -
- elt[row[1]][col[2]] * elt[row[2]][col[1]];
-
- float cofactor10 =
- elt[row[1]][col[2]] * elt[row[2]][col[0]] -
- elt[row[1]][col[0]] * elt[row[2]][col[2]];
-
- float cofactor20 =
- elt[row[1]][col[0]] * elt[row[2]][col[1]] -
- elt[row[1]][col[1]] * elt[row[2]][col[0]];
-
- // Product of the first row and the cofactors along the first row
- return
- elt[row[0]][col[0]] * cofactor00 +
- elt[row[0]][col[1]] * cofactor10 +
- elt[row[0]][col[2]] * cofactor20;
-}
-
-
-CoordinateFrame Matrix4::approxCoordinateFrame() const {
- CoordinateFrame cframe;
-
- for (int r = 0; r < 3; ++r) {
- for (int c = 0; c < 3; ++c) {
- cframe.rotation[r][c] = elt[r][c];
- }
- cframe.translation[r] = elt[r][3];
- }
-
- // Ensure that the rotation matrix is orthonormal
- cframe.rotation.orthonormalize();
-
- return cframe;
-}
-
-
-void Matrix4::serialize(class BinaryOutput& b) const {
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- b.writeFloat32(elt[r][c]);
- }
- }
-}
-
-
-void Matrix4::deserialize(class BinaryInput& b) {
- for (int r = 0; r < 4; ++r) {
- for (int c = 0; c < 4; ++c) {
- elt[r][c] = b.readFloat32();
- }
- }
-}
-
-std::string Matrix4::toString() const {
- return G3D::format("[%g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g]",
- elt[0][0], elt[0][1], elt[0][2], elt[0][3],
- elt[1][0], elt[1][1], elt[1][2], elt[1][3],
- elt[2][0], elt[2][1], elt[2][2], elt[2][3],
- elt[3][0], elt[3][1], elt[3][2], elt[3][3]);
-}
-
-} // namespace
-
-