#include "Mat3.h" NS_AX_MATH_BEGIN Mat3::Mat3() { loadIdentity(); } Mat3::Mat3(float m[9]) { this->m[0] = m[0]; this->m[1] = m[1]; this->m[2] = m[2]; this->m[3] = m[3]; this->m[4] = m[4]; this->m[5] = m[5]; this->m[6] = m[6]; this->m[7] = m[7]; this->m[8] = m[8]; } float Mat3::get(int i, int j) { switch (i) { case 0: switch (j) { case 0: return m[0]; case 1: return m[1]; case 2: return m[2]; } case 1: switch (j) { case 0: return m[3]; case 1: return m[4]; case 2: return m[5]; } case 2: switch (j) { case 0: return m[6]; case 1: return m[7]; case 2: return m[8]; } } return 0.0f; // throw new JmeException("Invalid indices into matrix."); } axis::Vec3 Mat3::getColumn(int i) { axis::Vec3 store; switch (i) { case 0: store.x = m[0]; store.y = m[3]; store.z = m[6]; break; case 1: store.x = m[1]; store.y = m[4]; store.z = m[7]; break; case 2: store.x = m[2]; store.y = m[5]; store.z = m[8]; break; default:; // logger.warning("Invalid column index."); // throw new JmeException("Invalid column index. " + i); } return store; } axis::Vec3 Mat3::getRow(int i) { axis::Vec3 store; switch (i) { case 0: store.x = m[0]; store.y = m[1]; store.z = m[2]; break; case 1: store.x = m[3]; store.y = m[4]; store.z = m[5]; break; case 2: store.x = m[6]; store.y = m[7]; store.z = m[8]; break; default:; // throw new JmeException("Invalid row index. " + i); } return store; } std::string Mat3::toString() { return ""; } void Mat3::setColumn(int i, const axis::Vec3& column) { switch (i) { case 0: m[0] = column.x; m[3] = column.y; m[6] = column.z; break; case 1: m[1] = column.x; m[4] = column.y; m[7] = column.z; break; case 2: m[2] = column.x; m[5] = column.y; m[8] = column.z; break; default:; // logger.warning("Invalid column index."); // throw new JmeException("Invalid column index. " + i); } } void Mat3::setRow(int i, const axis::Vec3& row) { switch (i) { case 0: m[0] = row.x; m[1] = row.y; m[2] = row.z; break; case 1: m[3] = row.x; m[4] = row.y; m[5] = row.z; break; case 2: m[6] = row.x; m[7] = row.y; m[8] = row.z; break; default:; // logger.warning("Invalid row index."); // throw new JmeException("Invalid row index. " + i); } } void Mat3::set(int i, int j, float value) { switch (i) { case 0: switch (j) { case 0: m[0] = value; return; case 1: m[1] = value; return; case 2: m[2] = value; return; } case 1: switch (j) { case 0: m[3] = value; return; case 1: m[4] = value; return; case 2: m[5] = value; return; } case 2: switch (j) { case 0: m[6] = value; return; case 1: m[7] = value; return; case 2: m[8] = value; return; } } // logger.warning("Invalid matrix index."); // throw new JmeException("Invalid indices into matrix."); } void Mat3::set(float matrix[3][3]) { // if (matrix.length != 3 || matrix[0].length != 3) { // throw new JmeException("Array must be of size 9."); // } m[0] = matrix[0][0]; m[1] = matrix[0][1]; m[2] = matrix[0][2]; m[3] = matrix[1][0]; m[4] = matrix[1][1]; m[5] = matrix[1][2]; m[6] = matrix[2][0]; m[7] = matrix[2][1]; m[8] = matrix[2][2]; } void Mat3::set(const axis::Vec3& uAxis, const axis::Vec3& vAxis, const axis::Vec3& wAxis) { m[0] = uAxis.x; m[3] = uAxis.y; m[6] = uAxis.z; m[1] = vAxis.x; m[4] = vAxis.y; m[7] = vAxis.z; m[2] = wAxis.x; m[5] = wAxis.y; m[8] = wAxis.z; } void Mat3::set(float matrix[9], bool rowMajor) { // if (matrix.length != 9) // throw new JmeException("Array must be of size 9."); if (rowMajor) { m[0] = matrix[0]; m[1] = matrix[1]; m[2] = matrix[2]; m[3] = matrix[3]; m[4] = matrix[4]; m[5] = matrix[5]; m[6] = matrix[6]; m[7] = matrix[7]; m[8] = matrix[8]; } else { m[0] = matrix[0]; m[1] = matrix[3]; m[2] = matrix[6]; m[3] = matrix[1]; m[4] = matrix[4]; m[5] = matrix[7]; m[6] = matrix[2]; m[7] = matrix[5]; m[8] = matrix[8]; } } void Mat3::loadIdentity() { m[1] = m[2] = m[3] = m[5] = m[6] = m[7] = 0; m[0] = m[4] = m[8] = 1; } bool Mat3::isIdentity() { return (m[0] == 1 && m[1] == 0 && m[2] == 0) && (m[3] == 0 && m[4] == 1 && m[5] == 0) && (m[6] == 0 && m[7] == 0 && m[8] == 1); } void Mat3::rotateX(float angle) { rotateX(std::sin(angle), std::cos(angle)); } void Mat3::rotateY(float angle) { rotateY(std::sin(angle), std::cos(angle)); } void Mat3::rotateZ(float angle) { rotateZ(std::sin(angle), std::cos(angle)); } void Mat3::rotateX(float s, float c) { Mat3 temp; temp.createRotationX(s, c); mult(temp); } void Mat3::rotateY(float s, float c) { Mat3 temp; temp.createRotationY(s, c); mult(temp); } void Mat3::rotateZ(float s, float c) { Mat3 temp; temp.createRotationZ(s, c); mult(temp); } void Mat3::createRotation(const axis::Vec3& axis, float fSin, float fCos) { float x = axis.x; float y = axis.y; float z = axis.z; // Make sure the input axis is normalized. float n = x * x + y * y + z * z; if (n != 1.0f) { // Not normalized. n = sqrt(n); // Prevent divide too close to zero. if (n > 0.000001f) { n = 1.0f / n; x *= n; y *= n; z *= n; } } float fOneMinusCos = ((float)1.0) - fCos; float fX2 = x * x; float fY2 = y * y; float fZ2 = z * z; float fXYM = x * y * fOneMinusCos; float fXZM = x * z * fOneMinusCos; float fYZM = y * z * fOneMinusCos; float fXSin = x * fSin; float fYSin = y * fSin; float fZSin = z * fSin; m[0] = fX2 * fOneMinusCos + fCos; m[1] = fXYM - fZSin; m[2] = fXZM + fYSin; m[3] = fXYM + fZSin; m[4] = fY2 * fOneMinusCos + fCos; m[5] = fYZM - fXSin; m[6] = fXZM - fYSin; m[7] = fYZM + fXSin; m[8] = fZ2 * fOneMinusCos + fCos; } void Mat3::createRotationX(float s, float c) { m[4] = c; m[5] = s; m[7] = -s; m[8] = c; } void Mat3::createRotationY(float s, float c) { m[0] = c; m[2] = -s; m[6] = s; m[8] = c; } void Mat3::createRotationZ(float s, float c) { m[0] = c; m[1] = s; m[3] = -s; m[4] = c; } Mat3& Mat3::mult(const Mat3& mat, Mat3& product) const { float temp00, temp01, temp02; float temp10, temp11, temp12; float temp20, temp21, temp22; temp00 = m[0] * mat.m[0] + m[1] * mat.m[3] + m[2] * mat.m[6]; temp01 = m[0] * mat.m[1] + m[1] * mat.m[4] + m[2] * mat.m[7]; temp02 = m[0] * mat.m[2] + m[1] * mat.m[5] + m[2] * mat.m[8]; temp10 = m[3] * mat.m[0] + m[4] * mat.m[3] + m[5] * mat.m[6]; temp11 = m[3] * mat.m[1] + m[4] * mat.m[4] + m[5] * mat.m[7]; temp12 = m[3] * mat.m[2] + m[4] * mat.m[5] + m[5] * mat.m[8]; temp20 = m[6] * mat.m[0] + m[7] * mat.m[3] + m[8] * mat.m[6]; temp21 = m[6] * mat.m[1] + m[7] * mat.m[4] + m[8] * mat.m[7]; temp22 = m[6] * mat.m[2] + m[7] * mat.m[5] + m[8] * mat.m[8]; product.m[0] = temp00; product.m[1] = temp01; product.m[2] = temp02; product.m[3] = temp10; product.m[4] = temp11; product.m[5] = temp12; product.m[6] = temp20; product.m[7] = temp21; product.m[8] = temp22; return product; } axis::Vec3 Mat3::mult(const axis::Vec3& vec) const { axis::Vec3 product; float x = vec.x; float y = vec.y; float z = vec.z; product.x = m[0] * x + m[1] * y + m[2] * z; product.y = m[3] * x + m[4] * y + m[5] * z; product.z = m[6] * x + m[7] * y + m[8] * z; return product; } Mat3& Mat3::multLocal(float scale) { m[0] *= scale; m[1] *= scale; m[2] *= scale; m[3] *= scale; m[4] *= scale; m[5] *= scale; m[6] *= scale; m[7] *= scale; m[8] *= scale; return *this; } Mat3& Mat3::addLocal(const Mat3& mat) { m[0] += mat.m[0]; m[1] += mat.m[1]; m[2] += mat.m[2]; m[3] += mat.m[3]; m[4] += mat.m[4]; m[5] += mat.m[5]; m[6] += mat.m[6]; m[7] += mat.m[7]; m[8] += mat.m[8]; return *this; } Mat3& Mat3::transposeLocal() { float tmp[9]; get(tmp, false); set(tmp, true); return *this; } Mat3 Mat3::invertNew(void) { Mat3 store; float det = determinant(); if (std::abs(det) <= 0) return store.zero(); store.m[0] = m[4] * m[8] - m[5] * m[7]; store.m[1] = m[2] * m[7] - m[1] * m[8]; store.m[2] = m[1] * m[5] - m[2] * m[4]; store.m[3] = m[5] * m[6] - m[3] * m[8]; store.m[4] = m[0] * m[8] - m[2] * m[6]; store.m[5] = m[2] * m[3] - m[0] * m[5]; store.m[6] = m[3] * m[7] - m[4] * m[6]; store.m[7] = m[1] * m[6] - m[0] * m[7]; store.m[8] = m[0] * m[4] - m[1] * m[3]; store.multLocal(1 / det); return store; } Mat3& Mat3::invertLocal() { float det = determinant(); if (std::abs(det) <= FLT_EPSILON) return zero(); float f00 = m[4] * m[8] - m[5] * m[7]; float f01 = m[2] * m[7] - m[1] * m[8]; float f02 = m[1] * m[5] - m[2] * m[4]; float f10 = m[5] * m[6] - m[3] * m[8]; float f11 = m[0] * m[8] - m[2] * m[6]; float f12 = m[2] * m[3] - m[0] * m[5]; float f20 = m[3] * m[7] - m[4] * m[6]; float f21 = m[1] * m[6] - m[0] * m[7]; float f22 = m[0] * m[4] - m[1] * m[3]; m[0] = f00; m[1] = f01; m[2] = f02; m[3] = f10; m[4] = f11; m[5] = f12; m[6] = f20; m[7] = f21; m[8] = f22; multLocal(1 / det); return *this; } Mat3 Mat3::adjoint() { Mat3 store; store.m[0] = m[4] * m[8] - m[5] * m[7]; store.m[1] = m[2] * m[7] - m[1] * m[8]; store.m[2] = m[1] * m[5] - m[2] * m[4]; store.m[3] = m[5] * m[6] - m[3] * m[8]; store.m[4] = m[0] * m[8] - m[2] * m[6]; store.m[5] = m[2] * m[3] - m[0] * m[5]; store.m[6] = m[3] * m[7] - m[4] * m[6]; store.m[7] = m[1] * m[6] - m[0] * m[7]; store.m[8] = m[0] * m[4] - m[1] * m[3]; return store; } float Mat3::determinant() { float fCo00 = m[4] * m[8] - m[5] * m[7]; float fCo10 = m[5] * m[6] - m[3] * m[8]; float fCo20 = m[3] * m[7] - m[4] * m[6]; float fDet = m[0] * fCo00 + m[1] * fCo10 + m[2] * fCo20; return fDet; } Mat3& Mat3::zero() { m[0] = m[1] = m[2] = m[3] = m[4] = m[5] = m[6] = m[7] = m[8] = 0.0f; return *this; } Mat3 Mat3::transposeNew() { float temp[9] = {m[0], m[3], m[6], m[1], m[4], m[7], m[2], m[5], m[8]}; return Mat3(temp); } bool Mat3::equals(const Mat3& o) const { return memcmp(&o, this, sizeof(o)) == 0; } void Mat3::fromStartEndVectors(axis::Vec3 start, axis::Vec3 end) { axis::Vec3 v; float e, h, f; axis::Vec3::cross(start, end, &v); e = start.dot(end); f = (e < 0) ? -e : e; // if "from" and "to" vectors are nearly parallel if (f > 1.0f - FLT_EPSILON) { axis::Vec3 u; axis::Vec3 x; float c1, c2, c3; /* coefficients for later use */ int i, j; x.x = (start.x > 0.0) ? start.x : -start.x; x.y = (start.y > 0.0) ? start.y : -start.y; x.z = (start.z > 0.0) ? start.z : -start.z; if (x.x < x.y) { if (x.x < x.z) { x.x = 1.0f; x.y = x.z = 0.0f; } else { x.z = 1.0f; x.x = x.y = 0.0f; } } else { if (x.y < x.z) { x.y = 1.0f; x.x = x.z = 0.0f; } else { x.z = 1.0f; x.x = x.y = 0.0f; } } u.x = x.x - start.x; u.y = x.y - start.y; u.z = x.z - start.z; v.x = x.x - end.x; v.y = x.y - end.y; v.z = x.z - end.z; c1 = 2.0f / u.dot(u); c2 = 2.0f / v.dot(v); c3 = c1 * c2 * u.dot(v); for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { float val = -c1 * (&u.x)[i] * (&u.x)[j] - c2 * (&v.x)[i] * (&v.x)[j] + c3 * (&v.x)[i] * (&u.x)[j]; set(i, j, val); } float val = get(i, i); set(i, i, val + 1.0f); } } else { // the most common case, unless "start"="end", or "start"=-"end" float hvx, hvz, hvxy, hvxz, hvyz; h = 1.0f / (1.0f + e); hvx = h * v.x; hvz = h * v.z; hvxy = hvx * v.y; hvxz = hvx * v.z; hvyz = hvz * v.y; set(0, 0, e + hvx * v.x); set(0, 1, hvxy - v.z); set(0, 2, hvxz + v.y); set(1, 0, hvxy + v.z); set(1, 1, e + h * v.y * v.y); set(1, 2, hvyz - v.x); set(2, 0, hvxz - v.y); set(2, 1, hvyz + v.x); set(2, 2, e + hvz * v.z); } } void Mat3::scale(const axis::Vec3& scale) { m[0] *= scale.x; m[3] *= scale.x; m[6] *= scale.x; m[1] *= scale.y; m[4] *= scale.y; m[7] *= scale.y; m[2] *= scale.z; m[5] *= scale.z; m[8] *= scale.z; } bool Mat3::equalIdentity(const Mat3& mat) { if (std::abs(mat.m[0] - 1) > 1e-4) return false; if (std::abs(mat.m[4] - 1) > 1e-4) return false; if (std::abs(mat.m[8] - 1) > 1e-4) return false; if (std::abs(mat.m[1]) > 1e-4) return false; if (std::abs(mat.m[2]) > 1e-4) return false; if (std::abs(mat.m[3]) > 1e-4) return false; if (std::abs(mat.m[5]) > 1e-4) return false; if (std::abs(mat.m[6]) > 1e-4) return false; if (std::abs(mat.m[7]) > 1e-4) return false; return true; } NS_AX_MATH_END