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-// Begin License:
-// Copyright (C) 2006-2014 Tobias Sargeant (tobias.sargeant@gmail.com).
-// All rights reserved.
-//
-// This file is part of the Carve CSG Library (http://carve-csg.com/)
-//
-// This file may be used under the terms of either the GNU General
-// Public License version 2 or 3 (at your option) as published by the
-// Free Software Foundation and appearing in the files LICENSE.GPL2
-// and LICENSE.GPL3 included in the packaging of this file.
-//
-// This file is provided "AS IS" with NO WARRANTY OF ANY KIND,
-// INCLUDING THE WARRANTIES OF DESIGN, MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE.
-// End:
-
-
-#pragma once
-
-#include <cstring>
-
-#include <carve/carve.hpp>
-
-#include <carve/math.hpp>
-#include <carve/geom.hpp>
-
-namespace carve {
- namespace math {
-
- struct Quaternion {
- double x, y, z, w;
-
- Quaternion(double _x, double _y, double _z, double _w) : x(_x), y(_y), z(_z), w(_w) {
- }
-
- Quaternion(double angle, const carve::geom::vector<3> &axis) {
- double s = axis.length();
- if (!carve::math::ZERO(s)) {
- double c = 1.0 / s;
- double omega = -0.5 * angle;
- s = sin(omega);
- x = axis.x * c * s;
- y = axis.y * c * s;
- z = axis.z * c * s;
- w = cos(omega);
- normalize();
- } else {
- x = y = z = 0.0;
- w = 1.0;
- }
- }
-
- double lengthSquared() const {
- return x * x + y * y + z * z + w * w;
- }
-
- double length() const {
- return sqrt(lengthSquared());
- }
-
- Quaternion normalized() const {
- return Quaternion(*this).normalize();
- }
-
- Quaternion &normalize() {
- double l = length();
- if (l == 0.0) {
- x = 1.0; y = 0.0; z = 0.0; w = 0.0;
- } else {
- x /= l; y /= l; z /= l; w /= l;
- }
- return *this;
- }
- };
-
- struct Matrix3 {
- // access: .m[col][row], .v[col * 4 + row], ._cr
- union {
- double m[3][3];
- double v[9];
- struct {
- // transposed
- double _11, _12, _13;
- double _21, _22, _23;
- double _31, _32, _33;
- };
- };
- Matrix3(double __11, double __21, double __31,
- double __12, double __22, double __32,
- double __13, double __23, double __33) {
- // nb, args are row major, storage is column major.
- _11 = __11; _12 = __12; _13 = __13;
- _21 = __21; _22 = __22; _23 = __23;
- _31 = __31; _32 = __32; _33 = __33;
- }
- Matrix3(double _m[3][3]) {
- std::memcpy(m, _m, sizeof(m));
- }
- Matrix3(double _v[9]) {
- std::memcpy(v, _v, sizeof(v));
- }
- Matrix3() {
- _11 = 1.00; _12 = 0.00; _13 = 0.00;
- _21 = 0.00; _22 = 1.00; _23 = 0.00;
- _31 = 0.00; _32 = 0.00; _33 = 1.00;
- }
- };
-
- struct Matrix {
- // access: .m[col][row], .v[col * 4 + row], ._cr
- union {
- double m[4][4];
- double v[16];
- struct {
- // transposed
- double _11, _12, _13, _14;
- double _21, _22, _23, _24;
- double _31, _32, _33, _34;
- double _41, _42 ,_43, _44;
- };
- };
- Matrix(double __11, double __21, double __31, double __41,
- double __12, double __22, double __32, double __42,
- double __13, double __23, double __33, double __43,
- double __14, double __24, double __34, double __44) {
- // nb, args are row major, storage is column major.
- _11 = __11; _12 = __12; _13 = __13; _14 = __14;
- _21 = __21; _22 = __22; _23 = __23; _24 = __24;
- _31 = __31; _32 = __32; _33 = __33; _34 = __34;
- _41 = __41; _42 = __42; _43 = __43; _44 = __44;
- }
- Matrix(double _m[4][4]) {
- std::memcpy(m, _m, sizeof(m));
- }
- Matrix(double _v[16]) {
- std::memcpy(v, _v, sizeof(v));
- }
- Matrix() {
- _11 = 1.00; _12 = 0.00; _13 = 0.00; _14 = 0.00;
- _21 = 0.00; _22 = 1.00; _23 = 0.00; _24 = 0.00;
- _31 = 0.00; _32 = 0.00; _33 = 1.00; _34 = 0.00;
- _41 = 0.00; _42 = 0.00; _43 = 0.00; _44 = 1.00;
- }
-
- static Matrix ROT(const Quaternion &q) {
- const double w = q.w;
- const double x = q.x;
- const double y = q.y;
- const double z = q.z;
- return Matrix(1 - 2*y*y - 2*z*z, 2*x*y - 2*z*w, 2*x*z + 2*y*w, 0.0,
- 2*x*y + 2*z*w, 1 - 2*x*x - 2*z*z, 2*y*z - 2*x*w, 0.0,
- 2*x*z - 2*y*w, 2*y*z + 2*x*w, 1 - 2*x*x - 2*y*y, 0.0,
- 0.0, 0.0, 0.0, 1.0);
- }
- static Matrix ROT(double angle, const carve::geom::vector<3> &axis) {
- return ROT(Quaternion(angle, axis));
- }
- static Matrix ROT(double angle, double x, double y, double z) {
- return ROT(Quaternion(angle, carve::geom::VECTOR(x, y, z)));
- }
- static Matrix TRANS(double x, double y, double z) {
- return Matrix(1.0, 0.0, 0.0, x,
- 0.0, 1.0, 0.0, y,
- 0.0, 0.0, 1.0, z,
- 0.0, 0.0, 0.0, 1.0);
- }
- static Matrix TRANS(const carve::geom::vector<3> &v) {
- return TRANS(v.x, v.y, v.z);
- }
- static Matrix SCALE(double x, double y, double z) {
- return Matrix(x, 0.0, 0.0, 0.0,
- 0.0, y, 0.0, 0.0,
- 0.0, 0.0, z, 0.0,
- 0.0, 0.0, 0.0, 1.0);
- }
- static Matrix SCALE(const carve::geom::vector<3> &v) {
- return SCALE(v.x, v.y, v.z);
- }
- static Matrix IDENT() {
- return Matrix(1.0, 0.0, 0.0, 0.0,
- 0.0, 1.0, 0.0, 0.0,
- 0.0, 0.0, 1.0, 0.0,
- 0.0, 0.0, 0.0, 1.0);
- }
- };
-
- static inline bool operator==(const Matrix &A, const Matrix &B) {
- for (size_t i = 0; i < 16; ++i) if (A.v[i] != B.v[i]) return false;
- return true;
- }
- static inline bool operator!=(const Matrix &A, const Matrix &B) {
- return !(A == B);
- }
- static inline carve::geom::vector<3> operator*(const Matrix &A, const carve::geom::vector<3> &b) {
- return carve::geom::VECTOR(
- A._11 * b.x + A._21 * b.y + A._31 * b.z + A._41,
- A._12 * b.x + A._22 * b.y + A._32 * b.z + A._42,
- A._13 * b.x + A._23 * b.y + A._33 * b.z + A._43
- );
- }
-
- static inline carve::geom::vector<3> &operator*=(carve::geom::vector<3> &b, const Matrix &A) {
- b = A * b;
- return b;
- }
-
- static inline carve::geom::vector<3> operator*(const Matrix3 &A, const carve::geom::vector<3> &b) {
- return carve::geom::VECTOR(
- A._11 * b.x + A._21 * b.y + A._31 * b.z,
- A._12 * b.x + A._22 * b.y + A._32 * b.z,
- A._13 * b.x + A._23 * b.y + A._33 * b.z
- );
- }
-
- static inline carve::geom::vector<3> &operator*=(carve::geom::vector<3> &b, const Matrix3 &A) {
- b = A * b;
- return b;
- }
-
- static inline Matrix operator*(const Matrix &A, const Matrix &B) {
- Matrix c;
- for (int i = 0; i < 4; i++) {
- for (int j = 0; j < 4; j++) {
- c.m[i][j] = 0.0;
- for (int k = 0; k < 4; k++) {
- c.m[i][j] += A.m[k][j] * B.m[i][k];
- }
- }
- }
- return c;
- }
-
- static inline Matrix3 operator*(const Matrix3 &A, const Matrix3 &B) {
- Matrix3 c;
- for (int i = 0; i < 3; i++) {
- for (int j = 0; j < 3; j++) {
- c.m[i][j] = 0.0;
- for (int k = 0; k < 3; k++) {
- c.m[i][j] += A.m[k][j] * B.m[i][k];
- }
- }
- }
- return c;
- }
-
-
-
- struct matrix_transformation {
- Matrix matrix;
-
- matrix_transformation(const Matrix &_matrix) : matrix(_matrix) {
- }
-
- carve::geom::vector<3> operator()(const carve::geom::vector<3> &vector) const {
- return matrix * vector;
- }
- };
-
-
-
- }
-}
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