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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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