aboutsummaryrefslogtreecommitdiff
path: root/shared
diff options
context:
space:
mode:
Diffstat (limited to 'shared')
-rw-r--r--shared/Matrices.cpp581
-rw-r--r--shared/Matrices.h909
-rw-r--r--shared/Vectors.h530
3 files changed, 2020 insertions, 0 deletions
diff --git a/shared/Matrices.cpp b/shared/Matrices.cpp
new file mode 100644
index 0000000..582b285
--- /dev/null
+++ b/shared/Matrices.cpp
@@ -0,0 +1,581 @@
+///////////////////////////////////////////////////////////////////////////////
+// Matrice.cpp
+// ===========
+// NxN Matrix Math classes
+//
+// The elements of the matrix are stored as column major order.
+// | 0 2 | | 0 3 6 | | 0 4 8 12 |
+// | 1 3 | | 1 4 7 | | 1 5 9 13 |
+// | 2 5 8 | | 2 6 10 14 |
+// | 3 7 11 15 |
+//
+// AUTHOR: Song Ho Ahn (song.ahn@gmail.com)
+// CREATED: 2005-06-24
+// UPDATED: 2014-09-21
+//
+// Copyright (C) 2005 Song Ho Ahn
+///////////////////////////////////////////////////////////////////////////////
+
+#include <cmath>
+#include <algorithm>
+#include "Matrices.h"
+
+const float DEG2RAD = 3.141593f / 180;
+const float EPSILON = 0.00001f;
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// transpose 2x2 matrix
+///////////////////////////////////////////////////////////////////////////////
+Matrix2& Matrix2::transpose()
+{
+ std::swap(m[1], m[2]);
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// return the determinant of 2x2 matrix
+///////////////////////////////////////////////////////////////////////////////
+float Matrix2::getDeterminant()
+{
+ return m[0] * m[3] - m[1] * m[2];
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inverse of 2x2 matrix
+// If cannot find inverse, set identity matrix
+///////////////////////////////////////////////////////////////////////////////
+Matrix2& Matrix2::invert()
+{
+ float determinant = getDeterminant();
+ if(fabs(determinant) <= EPSILON)
+ {
+ return identity();
+ }
+
+ float tmp = m[0]; // copy the first element
+ float invDeterminant = 1.0f / determinant;
+ m[0] = invDeterminant * m[3];
+ m[1] = -invDeterminant * m[1];
+ m[2] = -invDeterminant * m[2];
+ m[3] = invDeterminant * tmp;
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// transpose 3x3 matrix
+///////////////////////////////////////////////////////////////////////////////
+Matrix3& Matrix3::transpose()
+{
+ std::swap(m[1], m[3]);
+ std::swap(m[2], m[6]);
+ std::swap(m[5], m[7]);
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// return determinant of 3x3 matrix
+///////////////////////////////////////////////////////////////////////////////
+float Matrix3::getDeterminant()
+{
+ return m[0] * (m[4] * m[8] - m[5] * m[7]) -
+ m[1] * (m[3] * m[8] - m[5] * m[6]) +
+ m[2] * (m[3] * m[7] - m[4] * m[6]);
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inverse 3x3 matrix
+// If cannot find inverse, set identity matrix
+///////////////////////////////////////////////////////////////////////////////
+Matrix3& Matrix3::invert()
+{
+ float determinant, invDeterminant;
+ float tmp[9];
+
+ tmp[0] = m[4] * m[8] - m[5] * m[7];
+ tmp[1] = m[2] * m[7] - m[1] * m[8];
+ tmp[2] = m[1] * m[5] - m[2] * m[4];
+ tmp[3] = m[5] * m[6] - m[3] * m[8];
+ tmp[4] = m[0] * m[8] - m[2] * m[6];
+ tmp[5] = m[2] * m[3] - m[0] * m[5];
+ tmp[6] = m[3] * m[7] - m[4] * m[6];
+ tmp[7] = m[1] * m[6] - m[0] * m[7];
+ tmp[8] = m[0] * m[4] - m[1] * m[3];
+
+ // check determinant if it is 0
+ determinant = m[0] * tmp[0] + m[1] * tmp[3] + m[2] * tmp[6];
+ if(fabs(determinant) <= EPSILON)
+ {
+ return identity(); // cannot inverse, make it idenety matrix
+ }
+
+ // divide by the determinant
+ invDeterminant = 1.0f / determinant;
+ m[0] = invDeterminant * tmp[0];
+ m[1] = invDeterminant * tmp[1];
+ m[2] = invDeterminant * tmp[2];
+ m[3] = invDeterminant * tmp[3];
+ m[4] = invDeterminant * tmp[4];
+ m[5] = invDeterminant * tmp[5];
+ m[6] = invDeterminant * tmp[6];
+ m[7] = invDeterminant * tmp[7];
+ m[8] = invDeterminant * tmp[8];
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// transpose 4x4 matrix
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::transpose()
+{
+ std::swap(m[1], m[4]);
+ std::swap(m[2], m[8]);
+ std::swap(m[3], m[12]);
+ std::swap(m[6], m[9]);
+ std::swap(m[7], m[13]);
+ std::swap(m[11], m[14]);
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inverse 4x4 matrix
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::invert()
+{
+ // If the 4th row is [0,0,0,1] then it is affine matrix and
+ // it has no projective transformation.
+ if(m[3] == 0 && m[7] == 0 && m[11] == 0 && m[15] == 1)
+ this->invertAffine();
+ else
+ {
+ this->invertGeneral();
+ /*@@ invertProjective() is not optimized (slower than generic one)
+ if(fabs(m[0]*m[5] - m[1]*m[4]) > EPSILON)
+ this->invertProjective(); // inverse using matrix partition
+ else
+ this->invertGeneral(); // generalized inverse
+ */
+ }
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// compute the inverse of 4x4 Euclidean transformation matrix
+//
+// Euclidean transformation is translation, rotation, and reflection.
+// With Euclidean transform, only the position and orientation of the object
+// will be changed. Euclidean transform does not change the shape of an object
+// (no scaling). Length and angle are reserved.
+//
+// Use inverseAffine() if the matrix has scale and shear transformation.
+//
+// M = [ R | T ]
+// [ --+-- ] (R denotes 3x3 rotation/reflection matrix)
+// [ 0 | 1 ] (T denotes 1x3 translation matrix)
+//
+// y = M*x -> y = R*x + T -> x = R^-1*(y - T) -> x = R^T*y - R^T*T
+// (R is orthogonal, R^-1 = R^T)
+//
+// [ R | T ]-1 [ R^T | -R^T * T ] (R denotes 3x3 rotation matrix)
+// [ --+-- ] = [ ----+--------- ] (T denotes 1x3 translation)
+// [ 0 | 1 ] [ 0 | 1 ] (R^T denotes R-transpose)
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::invertEuclidean()
+{
+ // transpose 3x3 rotation matrix part
+ // | R^T | 0 |
+ // | ----+-- |
+ // | 0 | 1 |
+ float tmp;
+ tmp = m[1]; m[1] = m[4]; m[4] = tmp;
+ tmp = m[2]; m[2] = m[8]; m[8] = tmp;
+ tmp = m[6]; m[6] = m[9]; m[9] = tmp;
+
+ // compute translation part -R^T * T
+ // | 0 | -R^T x |
+ // | --+------- |
+ // | 0 | 0 |
+ float x = m[12];
+ float y = m[13];
+ float z = m[14];
+ m[12] = -(m[0] * x + m[4] * y + m[8] * z);
+ m[13] = -(m[1] * x + m[5] * y + m[9] * z);
+ m[14] = -(m[2] * x + m[6] * y + m[10]* z);
+
+ // last row should be unchanged (0,0,0,1)
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// compute the inverse of a 4x4 affine transformation matrix
+//
+// Affine transformations are generalizations of Euclidean transformations.
+// Affine transformation includes translation, rotation, reflection, scaling,
+// and shearing. Length and angle are NOT preserved.
+// M = [ R | T ]
+// [ --+-- ] (R denotes 3x3 rotation/scale/shear matrix)
+// [ 0 | 1 ] (T denotes 1x3 translation matrix)
+//
+// y = M*x -> y = R*x + T -> x = R^-1*(y - T) -> x = R^-1*y - R^-1*T
+//
+// [ R | T ]-1 [ R^-1 | -R^-1 * T ]
+// [ --+-- ] = [ -----+---------- ]
+// [ 0 | 1 ] [ 0 + 1 ]
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::invertAffine()
+{
+ // R^-1
+ Matrix3 r(m[0],m[1],m[2], m[4],m[5],m[6], m[8],m[9],m[10]);
+ r.invert();
+ m[0] = r[0]; m[1] = r[1]; m[2] = r[2];
+ m[4] = r[3]; m[5] = r[4]; m[6] = r[5];
+ m[8] = r[6]; m[9] = r[7]; m[10]= r[8];
+
+ // -R^-1 * T
+ float x = m[12];
+ float y = m[13];
+ float z = m[14];
+ m[12] = -(r[0] * x + r[3] * y + r[6] * z);
+ m[13] = -(r[1] * x + r[4] * y + r[7] * z);
+ m[14] = -(r[2] * x + r[5] * y + r[8] * z);
+
+ // last row should be unchanged (0,0,0,1)
+ //m[3] = m[7] = m[11] = 0.0f;
+ //m[15] = 1.0f;
+
+ return * this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inverse matrix using matrix partitioning (blockwise inverse)
+// It devides a 4x4 matrix into 4 of 2x2 matrices. It works in case of where
+// det(A) != 0. If not, use the generic inverse method
+// inverse formula.
+// M = [ A | B ] A, B, C, D are 2x2 matrix blocks
+// [ --+-- ] det(M) = |A| * |D - ((C * A^-1) * B)|
+// [ C | D ]
+//
+// M^-1 = [ A' | B' ] A' = A^-1 - (A^-1 * B) * C'
+// [ ---+--- ] B' = (A^-1 * B) * -D'
+// [ C' | D' ] C' = -D' * (C * A^-1)
+// D' = (D - ((C * A^-1) * B))^-1
+//
+// NOTE: I wrap with () if it it used more than once.
+// The matrix is invertable even if det(A)=0, so must check det(A) before
+// calling this function, and use invertGeneric() instead.
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::invertProjective()
+{
+ // partition
+ Matrix2 a(m[0], m[1], m[4], m[5]);
+ Matrix2 b(m[8], m[9], m[12], m[13]);
+ Matrix2 c(m[2], m[3], m[6], m[7]);
+ Matrix2 d(m[10], m[11], m[14], m[15]);
+
+ // pre-compute repeated parts
+ a.invert(); // A^-1
+ Matrix2 ab = a * b; // A^-1 * B
+ Matrix2 ca = c * a; // C * A^-1
+ Matrix2 cab = ca * b; // C * A^-1 * B
+ Matrix2 dcab = d - cab; // D - C * A^-1 * B
+
+ // check determinant if |D - C * A^-1 * B| = 0
+ //NOTE: this function assumes det(A) is already checked. if |A|=0 then,
+ // cannot use this function.
+ float determinant = dcab[0] * dcab[3] - dcab[1] * dcab[2];
+ if(fabs(determinant) <= EPSILON)
+ {
+ return identity();
+ }
+
+ // compute D' and -D'
+ Matrix2 d1 = dcab; // (D - C * A^-1 * B)
+ d1.invert(); // (D - C * A^-1 * B)^-1
+ Matrix2 d2 = -d1; // -(D - C * A^-1 * B)^-1
+
+ // compute C'
+ Matrix2 c1 = d2 * ca; // -D' * (C * A^-1)
+
+ // compute B'
+ Matrix2 b1 = ab * d2; // (A^-1 * B) * -D'
+
+ // compute A'
+ Matrix2 a1 = a - (ab * c1); // A^-1 - (A^-1 * B) * C'
+
+ // assemble inverse matrix
+ m[0] = a1[0]; m[4] = a1[2]; /*|*/ m[8] = b1[0]; m[12]= b1[2];
+ m[1] = a1[1]; m[5] = a1[3]; /*|*/ m[9] = b1[1]; m[13]= b1[3];
+ /*-----------------------------+-----------------------------*/
+ m[2] = c1[0]; m[6] = c1[2]; /*|*/ m[10]= d1[0]; m[14]= d1[2];
+ m[3] = c1[1]; m[7] = c1[3]; /*|*/ m[11]= d1[1]; m[15]= d1[3];
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// compute the inverse of a general 4x4 matrix using Cramer's Rule
+// If cannot find inverse, return indentity matrix
+// M^-1 = adj(M) / det(M)
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::invertGeneral()
+{
+ // get cofactors of minor matrices
+ float cofactor0 = getCofactor(m[5],m[6],m[7], m[9],m[10],m[11], m[13],m[14],m[15]);
+ float cofactor1 = getCofactor(m[4],m[6],m[7], m[8],m[10],m[11], m[12],m[14],m[15]);
+ float cofactor2 = getCofactor(m[4],m[5],m[7], m[8],m[9], m[11], m[12],m[13],m[15]);
+ float cofactor3 = getCofactor(m[4],m[5],m[6], m[8],m[9], m[10], m[12],m[13],m[14]);
+
+ // get determinant
+ float determinant = m[0] * cofactor0 - m[1] * cofactor1 + m[2] * cofactor2 - m[3] * cofactor3;
+ if(fabs(determinant) <= EPSILON)
+ {
+ return identity();
+ }
+
+ // get rest of cofactors for adj(M)
+ float cofactor4 = getCofactor(m[1],m[2],m[3], m[9],m[10],m[11], m[13],m[14],m[15]);
+ float cofactor5 = getCofactor(m[0],m[2],m[3], m[8],m[10],m[11], m[12],m[14],m[15]);
+ float cofactor6 = getCofactor(m[0],m[1],m[3], m[8],m[9], m[11], m[12],m[13],m[15]);
+ float cofactor7 = getCofactor(m[0],m[1],m[2], m[8],m[9], m[10], m[12],m[13],m[14]);
+
+ float cofactor8 = getCofactor(m[1],m[2],m[3], m[5],m[6], m[7], m[13],m[14],m[15]);
+ float cofactor9 = getCofactor(m[0],m[2],m[3], m[4],m[6], m[7], m[12],m[14],m[15]);
+ float cofactor10= getCofactor(m[0],m[1],m[3], m[4],m[5], m[7], m[12],m[13],m[15]);
+ float cofactor11= getCofactor(m[0],m[1],m[2], m[4],m[5], m[6], m[12],m[13],m[14]);
+
+ float cofactor12= getCofactor(m[1],m[2],m[3], m[5],m[6], m[7], m[9], m[10],m[11]);
+ float cofactor13= getCofactor(m[0],m[2],m[3], m[4],m[6], m[7], m[8], m[10],m[11]);
+ float cofactor14= getCofactor(m[0],m[1],m[3], m[4],m[5], m[7], m[8], m[9], m[11]);
+ float cofactor15= getCofactor(m[0],m[1],m[2], m[4],m[5], m[6], m[8], m[9], m[10]);
+
+ // build inverse matrix = adj(M) / det(M)
+ // adjugate of M is the transpose of the cofactor matrix of M
+ float invDeterminant = 1.0f / determinant;
+ m[0] = invDeterminant * cofactor0;
+ m[1] = -invDeterminant * cofactor4;
+ m[2] = invDeterminant * cofactor8;
+ m[3] = -invDeterminant * cofactor12;
+
+ m[4] = -invDeterminant * cofactor1;
+ m[5] = invDeterminant * cofactor5;
+ m[6] = -invDeterminant * cofactor9;
+ m[7] = invDeterminant * cofactor13;
+
+ m[8] = invDeterminant * cofactor2;
+ m[9] = -invDeterminant * cofactor6;
+ m[10]= invDeterminant * cofactor10;
+ m[11]= -invDeterminant * cofactor14;
+
+ m[12]= -invDeterminant * cofactor3;
+ m[13]= invDeterminant * cofactor7;
+ m[14]= -invDeterminant * cofactor11;
+ m[15]= invDeterminant * cofactor15;
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// return determinant of 4x4 matrix
+///////////////////////////////////////////////////////////////////////////////
+float Matrix4::getDeterminant()
+{
+ return m[0] * getCofactor(m[5],m[6],m[7], m[9],m[10],m[11], m[13],m[14],m[15]) -
+ m[1] * getCofactor(m[4],m[6],m[7], m[8],m[10],m[11], m[12],m[14],m[15]) +
+ m[2] * getCofactor(m[4],m[5],m[7], m[8],m[9], m[11], m[12],m[13],m[15]) -
+ m[3] * getCofactor(m[4],m[5],m[6], m[8],m[9], m[10], m[12],m[13],m[14]);
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// compute cofactor of 3x3 minor matrix without sign
+// input params are 9 elements of the minor matrix
+// NOTE: The caller must know its sign.
+///////////////////////////////////////////////////////////////////////////////
+float Matrix4::getCofactor(float m0, float m1, float m2,
+ float m3, float m4, float m5,
+ float m6, float m7, float m8)
+{
+ return m0 * (m4 * m8 - m5 * m7) -
+ m1 * (m3 * m8 - m5 * m6) +
+ m2 * (m3 * m7 - m4 * m6);
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// translate this matrix by (x, y, z)
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::translate(const Vector3& v)
+{
+ return translate(v.x, v.y, v.z);
+}
+
+Matrix4& Matrix4::translate(float x, float y, float z)
+{
+ m[0] += m[3] * x; m[4] += m[7] * x; m[8] += m[11]* x; m[12]+= m[15]* x;
+ m[1] += m[3] * y; m[5] += m[7] * y; m[9] += m[11]* y; m[13]+= m[15]* y;
+ m[2] += m[3] * z; m[6] += m[7] * z; m[10]+= m[11]* z; m[14]+= m[15]* z;
+
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// uniform scale
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::scale(float s)
+{
+ return scale(s, s, s);
+}
+
+Matrix4& Matrix4::scale(float x, float y, float z)
+{
+ m[0] *= x; m[4] *= x; m[8] *= x; m[12] *= x;
+ m[1] *= y; m[5] *= y; m[9] *= y; m[13] *= y;
+ m[2] *= z; m[6] *= z; m[10]*= z; m[14] *= z;
+ return *this;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// build a rotation matrix with given angle(degree) and rotation axis, then
+// multiply it with this object
+///////////////////////////////////////////////////////////////////////////////
+Matrix4& Matrix4::rotate(float angle, const Vector3& axis)
+{
+ return rotate(angle, axis.x, axis.y, axis.z);
+}
+
+Matrix4& Matrix4::rotate(float angle, float x, float y, float z)
+{
+ float c = cosf(angle * DEG2RAD); // cosine
+ float s = sinf(angle * DEG2RAD); // sine
+ float c1 = 1.0f - c; // 1 - c
+ float m0 = m[0], m4 = m[4], m8 = m[8], m12= m[12],
+ m1 = m[1], m5 = m[5], m9 = m[9], m13= m[13],
+ m2 = m[2], m6 = m[6], m10= m[10], m14= m[14];
+
+ // build rotation matrix
+ float r0 = x * x * c1 + c;
+ float r1 = x * y * c1 + z * s;
+ float r2 = x * z * c1 - y * s;
+ float r4 = x * y * c1 - z * s;
+ float r5 = y * y * c1 + c;
+ float r6 = y * z * c1 + x * s;
+ float r8 = x * z * c1 + y * s;
+ float r9 = y * z * c1 - x * s;
+ float r10= z * z * c1 + c;
+
+ // multiply rotation matrix
+ m[0] = r0 * m0 + r4 * m1 + r8 * m2;
+ m[1] = r1 * m0 + r5 * m1 + r9 * m2;
+ m[2] = r2 * m0 + r6 * m1 + r10* m2;
+ m[4] = r0 * m4 + r4 * m5 + r8 * m6;
+ m[5] = r1 * m4 + r5 * m5 + r9 * m6;
+ m[6] = r2 * m4 + r6 * m5 + r10* m6;
+ m[8] = r0 * m8 + r4 * m9 + r8 * m10;
+ m[9] = r1 * m8 + r5 * m9 + r9 * m10;
+ m[10]= r2 * m8 + r6 * m9 + r10* m10;
+ m[12]= r0 * m12+ r4 * m13+ r8 * m14;
+ m[13]= r1 * m12+ r5 * m13+ r9 * m14;
+ m[14]= r2 * m12+ r6 * m13+ r10* m14;
+
+ return *this;
+}
+
+Matrix4& Matrix4::rotateX(float angle)
+{
+ float c = cosf(angle * DEG2RAD);
+ float s = sinf(angle * DEG2RAD);
+ float m1 = m[1], m2 = m[2],
+ m5 = m[5], m6 = m[6],
+ m9 = m[9], m10= m[10],
+ m13= m[13], m14= m[14];
+
+ m[1] = m1 * c + m2 *-s;
+ m[2] = m1 * s + m2 * c;
+ m[5] = m5 * c + m6 *-s;
+ m[6] = m5 * s + m6 * c;
+ m[9] = m9 * c + m10*-s;
+ m[10]= m9 * s + m10* c;
+ m[13]= m13* c + m14*-s;
+ m[14]= m13* s + m14* c;
+
+ return *this;
+}
+
+Matrix4& Matrix4::rotateY(float angle)
+{
+ float c = cosf(angle * DEG2RAD);
+ float s = sinf(angle * DEG2RAD);
+ float m0 = m[0], m2 = m[2],
+ m4 = m[4], m6 = m[6],
+ m8 = m[8], m10= m[10],
+ m12= m[12], m14= m[14];
+
+ m[0] = m0 * c + m2 * s;
+ m[2] = m0 *-s + m2 * c;
+ m[4] = m4 * c + m6 * s;
+ m[6] = m4 *-s + m6 * c;
+ m[8] = m8 * c + m10* s;
+ m[10]= m8 *-s + m10* c;
+ m[12]= m12* c + m14* s;
+ m[14]= m12*-s + m14* c;
+
+ return *this;
+}
+
+Matrix4& Matrix4::rotateZ(float angle)
+{
+ float c = cosf(angle * DEG2RAD);
+ float s = sinf(angle * DEG2RAD);
+ float m0 = m[0], m1 = m[1],
+ m4 = m[4], m5 = m[5],
+ m8 = m[8], m9 = m[9],
+ m12= m[12], m13= m[13];
+
+ m[0] = m0 * c + m1 *-s;
+ m[1] = m0 * s + m1 * c;
+ m[4] = m4 * c + m5 *-s;
+ m[5] = m4 * s + m5 * c;
+ m[8] = m8 * c + m9 *-s;
+ m[9] = m8 * s + m9 * c;
+ m[12]= m12* c + m13*-s;
+ m[13]= m12* s + m13* c;
+
+ return *this;
+}
diff --git a/shared/Matrices.h b/shared/Matrices.h
new file mode 100644
index 0000000..3515f54
--- /dev/null
+++ b/shared/Matrices.h
@@ -0,0 +1,909 @@
+///////////////////////////////////////////////////////////////////////////////
+// Matrice.h
+// =========
+// NxN Matrix Math classes
+//
+// The elements of the matrix are stored as column major order.
+// | 0 2 | | 0 3 6 | | 0 4 8 12 |
+// | 1 3 | | 1 4 7 | | 1 5 9 13 |
+// | 2 5 8 | | 2 6 10 14 |
+// | 3 7 11 15 |
+//
+// AUTHOR: Song Ho Ahn (song.ahn@gmail.com)
+// CREATED: 2005-06-24
+// UPDATED: 2013-09-30
+//
+// Copyright (C) 2005 Song Ho Ahn
+///////////////////////////////////////////////////////////////////////////////
+
+#ifndef MATH_MATRICES_H
+#define MATH_MATRICES_H
+
+#include <iostream>
+#include <iomanip>
+#include "Vectors.h"
+
+///////////////////////////////////////////////////////////////////////////
+// 2x2 matrix
+///////////////////////////////////////////////////////////////////////////
+class Matrix2
+{
+public:
+ // constructors
+ Matrix2(); // init with identity
+ Matrix2(const float src[4]);
+ Matrix2(float m0, float m1, float m2, float m3);
+
+ void set(const float src[4]);
+ void set(float m0, float m1, float m2, float m3);
+ void setRow(int index, const float row[2]);
+ void setRow(int index, const Vector2& v);
+ void setColumn(int index, const float col[2]);
+ void setColumn(int index, const Vector2& v);
+
+ const float* get() const;
+ float getDeterminant();
+
+ Matrix2& identity();
+ Matrix2& transpose(); // transpose itself and return reference
+ Matrix2& invert();
+
+ // operators
+ Matrix2 operator+(const Matrix2& rhs) const; // add rhs
+ Matrix2 operator-(const Matrix2& rhs) const; // subtract rhs
+ Matrix2& operator+=(const Matrix2& rhs); // add rhs and update this object
+ Matrix2& operator-=(const Matrix2& rhs); // subtract rhs and update this object
+ Vector2 operator*(const Vector2& rhs) const; // multiplication: v' = M * v
+ Matrix2 operator*(const Matrix2& rhs) const; // multiplication: M3 = M1 * M2
+ Matrix2& operator*=(const Matrix2& rhs); // multiplication: M1' = M1 * M2
+ bool operator==(const Matrix2& rhs) const; // exact compare, no epsilon
+ bool operator!=(const Matrix2& rhs) const; // exact compare, no epsilon
+ float operator[](int index) const; // subscript operator v[0], v[1]
+ float& operator[](int index); // subscript operator v[0], v[1]
+
+ friend Matrix2 operator-(const Matrix2& m); // unary operator (-)
+ friend Matrix2 operator*(float scalar, const Matrix2& m); // pre-multiplication
+ friend Vector2 operator*(const Vector2& vec, const Matrix2& m); // pre-multiplication
+ friend std::ostream& operator<<(std::ostream& os, const Matrix2& m);
+
+protected:
+
+private:
+ float m[4];
+
+};
+
+
+
+///////////////////////////////////////////////////////////////////////////
+// 3x3 matrix
+///////////////////////////////////////////////////////////////////////////
+class Matrix3
+{
+public:
+ // constructors
+ Matrix3(); // init with identity
+ Matrix3(const float src[9]);
+ Matrix3(float m0, float m1, float m2, // 1st column
+ float m3, float m4, float m5, // 2nd column
+ float m6, float m7, float m8); // 3rd column
+
+ void set(const float src[9]);
+ void set(float m0, float m1, float m2, // 1st column
+ float m3, float m4, float m5, // 2nd column
+ float m6, float m7, float m8); // 3rd column
+ void setRow(int index, const float row[3]);
+ void setRow(int index, const Vector3& v);
+ void setColumn(int index, const float col[3]);
+ void setColumn(int index, const Vector3& v);
+
+ const float* get() const;
+ float getDeterminant();
+
+ Matrix3& identity();
+ Matrix3& transpose(); // transpose itself and return reference
+ Matrix3& invert();
+
+ // operators
+ Matrix3 operator+(const Matrix3& rhs) const; // add rhs
+ Matrix3 operator-(const Matrix3& rhs) const; // subtract rhs
+ Matrix3& operator+=(const Matrix3& rhs); // add rhs and update this object
+ Matrix3& operator-=(const Matrix3& rhs); // subtract rhs and update this object
+ Vector3 operator*(const Vector3& rhs) const; // multiplication: v' = M * v
+ Matrix3 operator*(const Matrix3& rhs) const; // multiplication: M3 = M1 * M2
+ Matrix3& operator*=(const Matrix3& rhs); // multiplication: M1' = M1 * M2
+ bool operator==(const Matrix3& rhs) const; // exact compare, no epsilon
+ bool operator!=(const Matrix3& rhs) const; // exact compare, no epsilon
+ float operator[](int index) const; // subscript operator v[0], v[1]
+ float& operator[](int index); // subscript operator v[0], v[1]
+
+ friend Matrix3 operator-(const Matrix3& m); // unary operator (-)
+ friend Matrix3 operator*(float scalar, const Matrix3& m); // pre-multiplication
+ friend Vector3 operator*(const Vector3& vec, const Matrix3& m); // pre-multiplication
+ friend std::ostream& operator<<(std::ostream& os, const Matrix3& m);
+
+protected:
+
+private:
+ float m[9];
+
+};
+
+
+
+///////////////////////////////////////////////////////////////////////////
+// 4x4 matrix
+///////////////////////////////////////////////////////////////////////////
+class Matrix4
+{
+public:
+ // constructors
+ Matrix4(); // init with identity
+ Matrix4(const float src[16]);
+ Matrix4(float m00, float m01, float m02, float m03, // 1st column
+ float m04, float m05, float m06, float m07, // 2nd column
+ float m08, float m09, float m10, float m11, // 3rd column
+ float m12, float m13, float m14, float m15);// 4th column
+
+ void set(const float src[16]);
+ void set(float m00, float m01, float m02, float m03, // 1st column
+ float m04, float m05, float m06, float m07, // 2nd column
+ float m08, float m09, float m10, float m11, // 3rd column
+ float m12, float m13, float m14, float m15);// 4th column
+ void setRow(int index, const float row[4]);
+ void setRow(int index, const Vector4& v);
+ void setRow(int index, const Vector3& v);
+ void setColumn(int index, const float col[4]);
+ void setColumn(int index, const Vector4& v);
+ void setColumn(int index, const Vector3& v);
+
+ const float* get() const;
+ const float* getTranspose(); // return transposed matrix
+ float getDeterminant();
+
+ Matrix4& identity();
+ Matrix4& transpose(); // transpose itself and return reference
+ Matrix4& invert(); // check best inverse method before inverse
+ Matrix4& invertEuclidean(); // inverse of Euclidean transform matrix
+ Matrix4& invertAffine(); // inverse of affine transform matrix
+ Matrix4& invertProjective(); // inverse of projective matrix using partitioning
+ Matrix4& invertGeneral(); // inverse of generic matrix
+
+ // transform matrix
+ Matrix4& translate(float x, float y, float z); // translation by (x,y,z)
+ Matrix4& translate(const Vector3& v); //
+ Matrix4& rotate(float angle, const Vector3& axis); // rotate angle(degree) along the given axix
+ Matrix4& rotate(float angle, float x, float y, float z);
+ Matrix4& rotateX(float angle); // rotate on X-axis with degree
+ Matrix4& rotateY(float angle); // rotate on Y-axis with degree
+ Matrix4& rotateZ(float angle); // rotate on Z-axis with degree
+ Matrix4& scale(float scale); // uniform scale
+ Matrix4& scale(float sx, float sy, float sz); // scale by (sx, sy, sz) on each axis
+
+ // operators
+ Matrix4 operator+(const Matrix4& rhs) const; // add rhs
+ Matrix4 operator-(const Matrix4& rhs) const; // subtract rhs
+ Matrix4& operator+=(const Matrix4& rhs); // add rhs and update this object
+ Matrix4& operator-=(const Matrix4& rhs); // subtract rhs and update this object
+ Vector4 operator*(const Vector4& rhs) const; // multiplication: v' = M * v
+ Vector3 operator*(const Vector3& rhs) const; // multiplication: v' = M * v
+ Matrix4 operator*(const Matrix4& rhs) const; // multiplication: M3 = M1 * M2
+ Matrix4& operator*=(const Matrix4& rhs); // multiplication: M1' = M1 * M2
+ bool operator==(const Matrix4& rhs) const; // exact compare, no epsilon
+ bool operator!=(const Matrix4& rhs) const; // exact compare, no epsilon
+ float operator[](int index) const; // subscript operator v[0], v[1]
+ float& operator[](int index); // subscript operator v[0], v[1]
+
+ friend Matrix4 operator-(const Matrix4& m); // unary operator (-)
+ friend Matrix4 operator*(float scalar, const Matrix4& m); // pre-multiplication
+ friend Vector3 operator*(const Vector3& vec, const Matrix4& m); // pre-multiplication
+ friend Vector4 operator*(const Vector4& vec, const Matrix4& m); // pre-multiplication
+ friend std::ostream& operator<<(std::ostream& os, const Matrix4& m);
+
+protected:
+
+private:
+ float getCofactor(float m0, float m1, float m2,
+ float m3, float m4, float m5,
+ float m6, float m7, float m8);
+
+ float m[16];
+ float tm[16]; // transpose m
+
+};
+
+
+
+///////////////////////////////////////////////////////////////////////////
+// inline functions for Matrix2
+///////////////////////////////////////////////////////////////////////////
+inline Matrix2::Matrix2()
+{
+ // initially identity matrix
+ identity();
+}
+
+
+
+inline Matrix2::Matrix2(const float src[4])
+{
+ set(src);
+}
+
+
+
+inline Matrix2::Matrix2(float m0, float m1, float m2, float m3)
+{
+ set(m0, m1, m2, m3);
+}
+
+
+
+inline void Matrix2::set(const float src[4])
+{
+ m[0] = src[0]; m[1] = src[1]; m[2] = src[2]; m[3] = src[3];
+}
+
+
+
+inline void Matrix2::set(float m0, float m1, float m2, float m3)
+{
+ m[0]= m0; m[1] = m1; m[2] = m2; m[3]= m3;
+}
+
+
+
+inline void Matrix2::setRow(int index, const float row[2])
+{
+ m[index] = row[0]; m[index + 2] = row[1];
+}
+
+
+
+inline void Matrix2::setRow(int index, const Vector2& v)
+{
+ m[index] = v.x; m[index + 2] = v.y;
+}
+
+
+
+inline void Matrix2::setColumn(int index, const float col[2])
+{
+ m[index*2] = col[0]; m[index*2 + 1] = col[1];
+}
+
+
+
+inline void Matrix2::setColumn(int index, const Vector2& v)
+{
+ m[index*2] = v.x; m[index*2 + 1] = v.y;
+}
+
+
+
+inline const float* Matrix2::get() const
+{
+ return m;
+}
+
+
+
+inline Matrix2& Matrix2::identity()
+{
+ m[0] = m[3] = 1.0f;
+ m[1] = m[2] = 0.0f;
+ return *this;
+}
+
+
+
+inline Matrix2 Matrix2::operator+(const Matrix2& rhs) const
+{
+ return Matrix2(m[0]+rhs[0], m[1]+rhs[1], m[2]+rhs[2], m[3]+rhs[3]);
+}
+
+
+
+inline Matrix2 Matrix2::operator-(const Matrix2& rhs) const
+{
+ return Matrix2(m[0]-rhs[0], m[1]-rhs[1], m[2]-rhs[2], m[3]-rhs[3]);
+}
+
+
+
+inline Matrix2& Matrix2::operator+=(const Matrix2& rhs)
+{
+ m[0] += rhs[0]; m[1] += rhs[1]; m[2] += rhs[2]; m[3] += rhs[3];
+ return *this;
+}
+
+
+
+inline Matrix2& Matrix2::operator-=(const Matrix2& rhs)
+{
+ m[0] -= rhs[0]; m[1] -= rhs[1]; m[2] -= rhs[2]; m[3] -= rhs[3];
+ return *this;
+}
+
+
+
+inline Vector2 Matrix2::operator*(const Vector2& rhs) const
+{
+ return Vector2(m[0]*rhs.x + m[2]*rhs.y, m[1]*rhs.x + m[3]*rhs.y);
+}
+
+
+
+inline Matrix2 Matrix2::operator*(const Matrix2& rhs) const
+{
+ return Matrix2(m[0]*rhs[0] + m[2]*rhs[1], m[1]*rhs[0] + m[3]*rhs[1],
+ m[0]*rhs[2] + m[2]*rhs[3], m[1]*rhs[2] + m[3]*rhs[3]);
+}
+
+
+
+inline Matrix2& Matrix2::operator*=(const Matrix2& rhs)
+{
+ *this = *this * rhs;
+ return *this;
+}
+
+
+
+inline bool Matrix2::operator==(const Matrix2& rhs) const
+{
+ return (m[0] == rhs[0]) && (m[1] == rhs[1]) && (m[2] == rhs[2]) && (m[3] == rhs[3]);
+}
+
+
+
+inline bool Matrix2::operator!=(const Matrix2& rhs) const
+{
+ return (m[0] != rhs[0]) || (m[1] != rhs[1]) || (m[2] != rhs[2]) || (m[3] != rhs[3]);
+}
+
+
+
+inline float Matrix2::operator[](int index) const
+{
+ return m[index];
+}
+
+
+
+inline float& Matrix2::operator[](int index)
+{
+ return m[index];
+}
+
+
+
+inline Matrix2 operator-(const Matrix2& rhs)
+{
+ return Matrix2(-rhs[0], -rhs[1], -rhs[2], -rhs[3]);
+}
+
+
+
+inline Matrix2 operator*(float s, const Matrix2& rhs)
+{
+ return Matrix2(s*rhs[0], s*rhs[1], s*rhs[2], s*rhs[3]);
+}
+
+
+
+inline Vector2 operator*(const Vector2& v, const Matrix2& rhs)
+{
+ return Vector2(v.x*rhs[0] + v.y*rhs[1], v.x*rhs[2] + v.y*rhs[3]);
+}
+
+
+
+inline std::ostream& operator<<(std::ostream& os, const Matrix2& m)
+{
+ os << std::fixed << std::setprecision(5);
+ os << "[" << std::setw(10) << m[0] << " " << std::setw(10) << m[2] << "]\n"
+ << "[" << std::setw(10) << m[1] << " " << std::setw(10) << m[3] << "]\n";
+ os << std::resetiosflags(std::ios_base::fixed | std::ios_base::floatfield);
+ return os;
+}
+// END OF MATRIX2 INLINE //////////////////////////////////////////////////////
+
+
+
+
+///////////////////////////////////////////////////////////////////////////
+// inline functions for Matrix3
+///////////////////////////////////////////////////////////////////////////
+inline Matrix3::Matrix3()
+{
+ // initially identity matrix
+ identity();
+}
+
+
+
+inline Matrix3::Matrix3(const float src[9])
+{
+ set(src);
+}
+
+
+
+inline Matrix3::Matrix3(float m0, float m1, float m2,
+ float m3, float m4, float m5,
+ float m6, float m7, float m8)
+{
+ set(m0, m1, m2, m3, m4, m5, m6, m7, m8);
+}
+
+
+
+inline void Matrix3::set(const float src[9])
+{
+ m[0] = src[0]; m[1] = src[1]; m[2] = src[2];
+ m[3] = src[3]; m[4] = src[4]; m[5] = src[5];
+ m[6] = src[6]; m[7] = src[7]; m[8] = src[8];
+}
+
+
+
+inline void Matrix3::set(float m0, float m1, float m2,
+ float m3, float m4, float m5,
+ float m6, float m7, float m8)
+{
+ m[0] = m0; m[1] = m1; m[2] = m2;
+ m[3] = m3; m[4] = m4; m[5] = m5;
+ m[6] = m6; m[7] = m7; m[8] = m8;
+}
+
+
+
+inline void Matrix3::setRow(int index, const float row[3])
+{
+ m[index] = row[0]; m[index + 3] = row[1]; m[index + 6] = row[2];
+}
+
+
+
+inline void Matrix3::setRow(int index, const Vector3& v)
+{
+ m[index] = v.x; m[index + 3] = v.y; m[index + 6] = v.z;
+}
+
+
+
+inline void Matrix3::setColumn(int index, const float col[3])
+{
+ m[index*3] = col[0]; m[index*3 + 1] = col[1]; m[index*3 + 2] = col[2];
+}
+
+
+
+inline void Matrix3::setColumn(int index, const Vector3& v)
+{
+ m[index*3] = v.x; m[index*3 + 1] = v.y; m[index*3 + 2] = v.z;
+}
+
+
+
+inline const float* Matrix3::get() const
+{
+ return m;
+}
+
+
+
+inline Matrix3& Matrix3::identity()
+{
+ m[0] = m[4] = m[8] = 1.0f;
+ m[1] = m[2] = m[3] = m[5] = m[6] = m[7] = 0.0f;
+ return *this;
+}
+
+
+
+inline Matrix3 Matrix3::operator+(const Matrix3& rhs) const
+{
+ return Matrix3(m[0]+rhs[0], m[1]+rhs[1], m[2]+rhs[2],
+ m[3]+rhs[3], m[4]+rhs[4], m[5]+rhs[5],
+ m[6]+rhs[6], m[7]+rhs[7], m[8]+rhs[8]);
+}
+
+
+
+inline Matrix3 Matrix3::operator-(const Matrix3& rhs) const
+{
+ return Matrix3(m[0]-rhs[0], m[1]-rhs[1], m[2]-rhs[2],
+ m[3]-rhs[3], m[4]-rhs[4], m[5]-rhs[5],
+ m[6]-rhs[6], m[7]-rhs[7], m[8]-rhs[8]);
+}
+
+
+
+inline Matrix3& Matrix3::operator+=(const Matrix3& rhs)
+{
+ m[0] += rhs[0]; m[1] += rhs[1]; m[2] += rhs[2];
+ m[3] += rhs[3]; m[4] += rhs[4]; m[5] += rhs[5];
+ m[6] += rhs[6]; m[7] += rhs[7]; m[8] += rhs[8];
+ return *this;
+}
+
+
+
+inline Matrix3& Matrix3::operator-=(const Matrix3& rhs)
+{
+ m[0] -= rhs[0]; m[1] -= rhs[1]; m[2] -= rhs[2];
+ m[3] -= rhs[3]; m[4] -= rhs[4]; m[5] -= rhs[5];
+ m[6] -= rhs[6]; m[7] -= rhs[7]; m[8] -= rhs[8];
+ return *this;
+}
+
+
+
+inline Vector3 Matrix3::operator*(const Vector3& rhs) const
+{
+ return Vector3(m[0]*rhs.x + m[3]*rhs.y + m[6]*rhs.z,
+ m[1]*rhs.x + m[4]*rhs.y + m[7]*rhs.z,
+ m[2]*rhs.x + m[5]*rhs.y + m[8]*rhs.z);
+}
+
+
+
+inline Matrix3 Matrix3::operator*(const Matrix3& rhs) const
+{
+ return Matrix3(m[0]*rhs[0] + m[3]*rhs[1] + m[6]*rhs[2], m[1]*rhs[0] + m[4]*rhs[1] + m[7]*rhs[2], m[2]*rhs[0] + m[5]*rhs[1] + m[8]*rhs[2],
+ m[0]*rhs[3] + m[3]*rhs[4] + m[6]*rhs[5], m[1]*rhs[3] + m[4]*rhs[4] + m[7]*rhs[5], m[2]*rhs[3] + m[5]*rhs[4] + m[8]*rhs[5],
+ m[0]*rhs[6] + m[3]*rhs[7] + m[6]*rhs[8], m[1]*rhs[6] + m[4]*rhs[7] + m[7]*rhs[8], m[2]*rhs[6] + m[5]*rhs[7] + m[8]*rhs[8]);
+}
+
+
+
+inline Matrix3& Matrix3::operator*=(const Matrix3& rhs)
+{
+ *this = *this * rhs;
+ return *this;
+}
+
+
+
+inline bool Matrix3::operator==(const Matrix3& rhs) const
+{
+ return (m[0] == rhs[0]) && (m[1] == rhs[1]) && (m[2] == rhs[2]) &&
+ (m[3] == rhs[3]) && (m[4] == rhs[4]) && (m[5] == rhs[5]) &&
+ (m[6] == rhs[6]) && (m[7] == rhs[7]) && (m[8] == rhs[8]);
+}
+
+
+
+inline bool Matrix3::operator!=(const Matrix3& rhs) const
+{
+ return (m[0] != rhs[0]) || (m[1] != rhs[1]) || (m[2] != rhs[2]) ||
+ (m[3] != rhs[3]) || (m[4] != rhs[4]) || (m[5] != rhs[5]) ||
+ (m[6] != rhs[6]) || (m[7] != rhs[7]) || (m[8] != rhs[8]);
+}
+
+
+
+inline float Matrix3::operator[](int index) const
+{
+ return m[index];
+}
+
+
+
+inline float& Matrix3::operator[](int index)
+{
+ return m[index];
+}
+
+
+
+inline Matrix3 operator-(const Matrix3& rhs)
+{
+ return Matrix3(-rhs[0], -rhs[1], -rhs[2], -rhs[3], -rhs[4], -rhs[5], -rhs[6], -rhs[7], -rhs[8]);
+}
+
+
+
+inline Matrix3 operator*(float s, const Matrix3& rhs)
+{
+ return Matrix3(s*rhs[0], s*rhs[1], s*rhs[2], s*rhs[3], s*rhs[4], s*rhs[5], s*rhs[6], s*rhs[7], s*rhs[8]);
+}
+
+
+
+inline Vector3 operator*(const Vector3& v, const Matrix3& m)
+{
+ return Vector3(v.x*m[0] + v.y*m[1] + v.z*m[2], v.x*m[3] + v.y*m[4] + v.z*m[5], v.x*m[6] + v.y*m[7] + v.z*m[8]);
+}
+
+
+
+inline std::ostream& operator<<(std::ostream& os, const Matrix3& m)
+{
+ os << std::fixed << std::setprecision(5);
+ os << "[" << std::setw(10) << m[0] << " " << std::setw(10) << m[3] << " " << std::setw(10) << m[6] << "]\n"
+ << "[" << std::setw(10) << m[1] << " " << std::setw(10) << m[4] << " " << std::setw(10) << m[7] << "]\n"
+ << "[" << std::setw(10) << m[2] << " " << std::setw(10) << m[5] << " " << std::setw(10) << m[8] << "]\n";
+ os << std::resetiosflags(std::ios_base::fixed | std::ios_base::floatfield);
+ return os;
+}
+// END OF MATRIX3 INLINE //////////////////////////////////////////////////////
+
+
+
+
+///////////////////////////////////////////////////////////////////////////
+// inline functions for Matrix4
+///////////////////////////////////////////////////////////////////////////
+inline Matrix4::Matrix4()
+{
+ // initially identity matrix
+ identity();
+}
+
+
+
+inline Matrix4::Matrix4(const float src[16])
+{
+ set(src);
+}
+
+
+
+inline Matrix4::Matrix4(float m00, float m01, float m02, float m03,
+ float m04, float m05, float m06, float m07,
+ float m08, float m09, float m10, float m11,
+ float m12, float m13, float m14, float m15)
+{
+ set(m00, m01, m02, m03, m04, m05, m06, m07, m08, m09, m10, m11, m12, m13, m14, m15);
+}
+
+
+
+inline void Matrix4::set(const float src[16])
+{
+ m[0] = src[0]; m[1] = src[1]; m[2] = src[2]; m[3] = src[3];
+ m[4] = src[4]; m[5] = src[5]; m[6] = src[6]; m[7] = src[7];
+ m[8] = src[8]; m[9] = src[9]; m[10]= src[10]; m[11]= src[11];
+ m[12]= src[12]; m[13]= src[13]; m[14]= src[14]; m[15]= src[15];
+}
+
+
+
+inline void Matrix4::set(float m00, float m01, float m02, float m03,
+ float m04, float m05, float m06, float m07,
+ float m08, float m09, float m10, float m11,
+ float m12, float m13, float m14, float m15)
+{
+ m[0] = m00; m[1] = m01; m[2] = m02; m[3] = m03;
+ m[4] = m04; m[5] = m05; m[6] = m06; m[7] = m07;
+ m[8] = m08; m[9] = m09; m[10]= m10; m[11]= m11;
+ m[12]= m12; m[13]= m13; m[14]= m14; m[15]= m15;
+}
+
+
+
+inline void Matrix4::setRow(int index, const float row[4])
+{
+ m[index] = row[0]; m[index + 4] = row[1]; m[index + 8] = row[2]; m[index + 12] = row[3];
+}
+
+
+
+inline void Matrix4::setRow(int index, const Vector4& v)
+{
+ m[index] = v.x; m[index + 4] = v.y; m[index + 8] = v.z; m[index + 12] = v.w;
+}
+
+
+
+inline void Matrix4::setRow(int index, const Vector3& v)
+{
+ m[index] = v.x; m[index + 4] = v.y; m[index + 8] = v.z;
+}
+
+
+
+inline void Matrix4::setColumn(int index, const float col[4])
+{
+ m[index*4] = col[0]; m[index*4 + 1] = col[1]; m[index*4 + 2] = col[2]; m[index*4 + 3] = col[3];
+}
+
+
+
+inline void Matrix4::setColumn(int index, const Vector4& v)
+{
+ m[index*4] = v.x; m[index*4 + 1] = v.y; m[index*4 + 2] = v.z; m[index*4 + 3] = v.w;
+}
+
+
+
+inline void Matrix4::setColumn(int index, const Vector3& v)
+{
+ m[index*4] = v.x; m[index*4 + 1] = v.y; m[index*4 + 2] = v.z;
+}
+
+
+
+inline const float* Matrix4::get() const
+{
+ return m;
+}
+
+
+
+inline const float* Matrix4::getTranspose()
+{
+ tm[0] = m[0]; tm[1] = m[4]; tm[2] = m[8]; tm[3] = m[12];
+ tm[4] = m[1]; tm[5] = m[5]; tm[6] = m[9]; tm[7] = m[13];
+ tm[8] = m[2]; tm[9] = m[6]; tm[10]= m[10]; tm[11]= m[14];
+ tm[12]= m[3]; tm[13]= m[7]; tm[14]= m[11]; tm[15]= m[15];
+ return tm;
+}
+
+
+
+inline Matrix4& Matrix4::identity()
+{
+ m[0] = m[5] = m[10] = m[15] = 1.0f;
+ m[1] = m[2] = m[3] = m[4] = m[6] = m[7] = m[8] = m[9] = m[11] = m[12] = m[13] = m[14] = 0.0f;
+ return *this;
+}
+
+
+
+inline Matrix4 Matrix4::operator+(const Matrix4& rhs) const
+{
+ return Matrix4(m[0]+rhs[0], m[1]+rhs[1], m[2]+rhs[2], m[3]+rhs[3],
+ m[4]+rhs[4], m[5]+rhs[5], m[6]+rhs[6], m[7]+rhs[7],
+ m[8]+rhs[8], m[9]+rhs[9], m[10]+rhs[10], m[11]+rhs[11],
+ m[12]+rhs[12], m[13]+rhs[13], m[14]+rhs[14], m[15]+rhs[15]);
+}
+
+
+
+inline Matrix4 Matrix4::operator-(const Matrix4& rhs) const
+{
+ return Matrix4(m[0]-rhs[0], m[1]-rhs[1], m[2]-rhs[2], m[3]-rhs[3],
+ m[4]-rhs[4], m[5]-rhs[5], m[6]-rhs[6], m[7]-rhs[7],
+ m[8]-rhs[8], m[9]-rhs[9], m[10]-rhs[10], m[11]-rhs[11],
+ m[12]-rhs[12], m[13]-rhs[13], m[14]-rhs[14], m[15]-rhs[15]);
+}
+
+
+
+inline Matrix4& Matrix4::operator+=(const Matrix4& rhs)
+{
+ m[0] += rhs[0]; m[1] += rhs[1]; m[2] += rhs[2]; m[3] += rhs[3];
+ m[4] += rhs[4]; m[5] += rhs[5]; m[6] += rhs[6]; m[7] += rhs[7];
+ m[8] += rhs[8]; m[9] += rhs[9]; m[10]+= rhs[10]; m[11]+= rhs[11];
+ m[12]+= rhs[12]; m[13]+= rhs[13]; m[14]+= rhs[14]; m[15]+= rhs[15];
+ return *this;
+}
+
+
+
+inline Matrix4& Matrix4::operator-=(const Matrix4& rhs)
+{
+ m[0] -= rhs[0]; m[1] -= rhs[1]; m[2] -= rhs[2]; m[3] -= rhs[3];
+ m[4] -= rhs[4]; m[5] -= rhs[5]; m[6] -= rhs[6]; m[7] -= rhs[7];
+ m[8] -= rhs[8]; m[9] -= rhs[9]; m[10]-= rhs[10]; m[11]-= rhs[11];
+ m[12]-= rhs[12]; m[13]-= rhs[13]; m[14]-= rhs[14]; m[15]-= rhs[15];
+ return *this;
+}
+
+
+
+inline Vector4 Matrix4::operator*(const Vector4& rhs) const
+{
+ return Vector4(m[0]*rhs.x + m[4]*rhs.y + m[8]*rhs.z + m[12]*rhs.w,
+ m[1]*rhs.x + m[5]*rhs.y + m[9]*rhs.z + m[13]*rhs.w,
+ m[2]*rhs.x + m[6]*rhs.y + m[10]*rhs.z + m[14]*rhs.w,
+ m[3]*rhs.x + m[7]*rhs.y + m[11]*rhs.z + m[15]*rhs.w);
+}
+
+
+
+inline Vector3 Matrix4::operator*(const Vector3& rhs) const
+{
+ return Vector3(m[0]*rhs.x + m[4]*rhs.y + m[8]*rhs.z,
+ m[1]*rhs.x + m[5]*rhs.y + m[9]*rhs.z,
+ m[2]*rhs.x + m[6]*rhs.y + m[10]*rhs.z);
+}
+
+
+
+inline Matrix4 Matrix4::operator*(const Matrix4& n) const
+{
+ return Matrix4(m[0]*n[0] + m[4]*n[1] + m[8]*n[2] + m[12]*n[3], m[1]*n[0] + m[5]*n[1] + m[9]*n[2] + m[13]*n[3], m[2]*n[0] + m[6]*n[1] + m[10]*n[2] + m[14]*n[3], m[3]*n[0] + m[7]*n[1] + m[11]*n[2] + m[15]*n[3],
+ m[0]*n[4] + m[4]*n[5] + m[8]*n[6] + m[12]*n[7], m[1]*n[4] + m[5]*n[5] + m[9]*n[6] + m[13]*n[7], m[2]*n[4] + m[6]*n[5] + m[10]*n[6] + m[14]*n[7], m[3]*n[4] + m[7]*n[5] + m[11]*n[6] + m[15]*n[7],
+ m[0]*n[8] + m[4]*n[9] + m[8]*n[10] + m[12]*n[11], m[1]*n[8] + m[5]*n[9] + m[9]*n[10] + m[13]*n[11], m[2]*n[8] + m[6]*n[9] + m[10]*n[10] + m[14]*n[11], m[3]*n[8] + m[7]*n[9] + m[11]*n[10] + m[15]*n[11],
+ m[0]*n[12] + m[4]*n[13] + m[8]*n[14] + m[12]*n[15], m[1]*n[12] + m[5]*n[13] + m[9]*n[14] + m[13]*n[15], m[2]*n[12] + m[6]*n[13] + m[10]*n[14] + m[14]*n[15], m[3]*n[12] + m[7]*n[13] + m[11]*n[14] + m[15]*n[15]);
+}
+
+
+
+inline Matrix4& Matrix4::operator*=(const Matrix4& rhs)
+{
+ *this = *this * rhs;
+ return *this;
+}
+
+
+
+inline bool Matrix4::operator==(const Matrix4& n) const
+{
+ return (m[0] == n[0]) && (m[1] == n[1]) && (m[2] == n[2]) && (m[3] == n[3]) &&
+ (m[4] == n[4]) && (m[5] == n[5]) && (m[6] == n[6]) && (m[7] == n[7]) &&
+ (m[8] == n[8]) && (m[9] == n[9]) && (m[10]== n[10]) && (m[11]== n[11]) &&
+ (m[12]== n[12]) && (m[13]== n[13]) && (m[14]== n[14]) && (m[15]== n[15]);
+}
+
+
+
+inline bool Matrix4::operator!=(const Matrix4& n) const
+{
+ return (m[0] != n[0]) || (m[1] != n[1]) || (m[2] != n[2]) || (m[3] != n[3]) ||
+ (m[4] != n[4]) || (m[5] != n[5]) || (m[6] != n[6]) || (m[7] != n[7]) ||
+ (m[8] != n[8]) || (m[9] != n[9]) || (m[10]!= n[10]) || (m[11]!= n[11]) ||
+ (m[12]!= n[12]) || (m[13]!= n[13]) || (m[14]!= n[14]) || (m[15]!= n[15]);
+}
+
+
+
+inline float Matrix4::operator[](int index) const
+{
+ return m[index];
+}
+
+
+
+inline float& Matrix4::operator[](int index)
+{
+ return m[index];
+}
+
+
+
+inline Matrix4 operator-(const Matrix4& rhs)
+{
+ return Matrix4(-rhs[0], -rhs[1], -rhs[2], -rhs[3], -rhs[4], -rhs[5], -rhs[6], -rhs[7], -rhs[8], -rhs[9], -rhs[10], -rhs[11], -rhs[12], -rhs[13], -rhs[14], -rhs[15]);
+}
+
+
+
+inline Matrix4 operator*(float s, const Matrix4& rhs)
+{
+ return Matrix4(s*rhs[0], s*rhs[1], s*rhs[2], s*rhs[3], s*rhs[4], s*rhs[5], s*rhs[6], s*rhs[7], s*rhs[8], s*rhs[9], s*rhs[10], s*rhs[11], s*rhs[12], s*rhs[13], s*rhs[14], s*rhs[15]);
+}
+
+
+
+inline Vector4 operator*(const Vector4& v, const Matrix4& m)
+{
+ return Vector4(v.x*m[0] + v.y*m[1] + v.z*m[2] + v.w*m[3], v.x*m[4] + v.y*m[5] + v.z*m[6] + v.w*m[7], v.x*m[8] + v.y*m[9] + v.z*m[10] + v.w*m[11], v.x*m[12] + v.y*m[13] + v.z*m[14] + v.w*m[15]);
+}
+
+
+
+inline Vector3 operator*(const Vector3& v, const Matrix4& m)
+{
+ return Vector3(v.x*m[0] + v.y*m[1] + v.z*m[2], v.x*m[4] + v.y*m[5] + v.z*m[6], v.x*m[8] + v.y*m[9] + v.z*m[10]);
+}
+
+
+
+inline std::ostream& operator<<(std::ostream& os, const Matrix4& m)
+{
+ os << std::fixed << std::setprecision(5);
+ os << "[" << std::setw(10) << m[0] << " " << std::setw(10) << m[4] << " " << std::setw(10) << m[8] << " " << std::setw(10) << m[12] << "]\n"
+ << "[" << std::setw(10) << m[1] << " " << std::setw(10) << m[5] << " " << std::setw(10) << m[9] << " " << std::setw(10) << m[13] << "]\n"
+ << "[" << std::setw(10) << m[2] << " " << std::setw(10) << m[6] << " " << std::setw(10) << m[10] << " " << std::setw(10) << m[14] << "]\n"
+ << "[" << std::setw(10) << m[3] << " " << std::setw(10) << m[7] << " " << std::setw(10) << m[11] << " " << std::setw(10) << m[15] << "]\n";
+ os << std::resetiosflags(std::ios_base::fixed | std::ios_base::floatfield);
+ return os;
+}
+// END OF MATRIX4 INLINE //////////////////////////////////////////////////////
+#endif
diff --git a/shared/Vectors.h b/shared/Vectors.h
new file mode 100644
index 0000000..2efb840
--- /dev/null
+++ b/shared/Vectors.h
@@ -0,0 +1,530 @@
+///////////////////////////////////////////////////////////////////////////////
+// Vectors.h
+// =========
+// 2D/3D/4D vectors
+//
+// AUTHOR: Song Ho Ahn (song.ahn@gmail.com)
+// CREATED: 2007-02-14
+// UPDATED: 2013-01-20
+//
+// Copyright (C) 2007-2013 Song Ho Ahn
+///////////////////////////////////////////////////////////////////////////////
+
+
+#ifndef VECTORS_H_DEF
+#define VECTORS_H_DEF
+
+#include <cmath>
+#include <iostream>
+
+///////////////////////////////////////////////////////////////////////////////
+// 2D vector
+///////////////////////////////////////////////////////////////////////////////
+struct Vector2
+{
+ float x;
+ float y;
+
+ // ctors
+ Vector2() : x(0), y(0) {};
+ Vector2(float x, float y) : x(x), y(y) {};
+
+ // utils functions
+ void set(float x, float y);
+ float length() const; //
+ float distance(const Vector2& vec) const; // distance between two vectors
+ Vector2& normalize(); //
+ float dot(const Vector2& vec) const; // dot product
+ bool equal(const Vector2& vec, float e) const; // compare with epsilon
+
+ // operators
+ Vector2 operator-() const; // unary operator (negate)
+ Vector2 operator+(const Vector2& rhs) const; // add rhs
+ Vector2 operator-(const Vector2& rhs) const; // subtract rhs
+ Vector2& operator+=(const Vector2& rhs); // add rhs and update this object
+ Vector2& operator-=(const Vector2& rhs); // subtract rhs and update this object
+ Vector2 operator*(const float scale) const; // scale
+ Vector2 operator*(const Vector2& rhs) const; // multiply each element
+ Vector2& operator*=(const float scale); // scale and update this object
+ Vector2& operator*=(const Vector2& rhs); // multiply each element and update this object
+ Vector2 operator/(const float scale) const; // inverse scale
+ Vector2& operator/=(const float scale); // scale and update this object
+ bool operator==(const Vector2& rhs) const; // exact compare, no epsilon
+ bool operator!=(const Vector2& rhs) const; // exact compare, no epsilon
+ bool operator<(const Vector2& rhs) const; // comparison for sort
+ float operator[](int index) const; // subscript operator v[0], v[1]
+ float& operator[](int index); // subscript operator v[0], v[1]
+
+ friend Vector2 operator*(const float a, const Vector2 vec);
+ friend std::ostream& operator<<(std::ostream& os, const Vector2& vec);
+};
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// 3D vector
+///////////////////////////////////////////////////////////////////////////////
+struct Vector3
+{
+ float x;
+ float y;
+ float z;
+
+ // ctors
+ Vector3() : x(0), y(0), z(0) {};
+ Vector3(float x, float y, float z) : x(x), y(y), z(z) {};
+
+ // utils functions
+ void set(float x, float y, float z);
+ float length() const; //
+ float distance(const Vector3& vec) const; // distance between two vectors
+ Vector3& normalize(); //
+ float dot(const Vector3& vec) const; // dot product
+ Vector3 cross(const Vector3& vec) const; // cross product
+ bool equal(const Vector3& vec, float e) const; // compare with epsilon
+
+ // operators
+ Vector3 operator-() const; // unary operator (negate)
+ Vector3 operator+(const Vector3& rhs) const; // add rhs
+ Vector3 operator-(const Vector3& rhs) const; // subtract rhs
+ Vector3& operator+=(const Vector3& rhs); // add rhs and update this object
+ Vector3& operator-=(const Vector3& rhs); // subtract rhs and update this object
+ Vector3 operator*(const float scale) const; // scale
+ Vector3 operator*(const Vector3& rhs) const; // multiplay each element
+ Vector3& operator*=(const float scale); // scale and update this object
+ Vector3& operator*=(const Vector3& rhs); // product each element and update this object
+ Vector3 operator/(const float scale) const; // inverse scale
+ Vector3& operator/=(const float scale); // scale and update this object
+ bool operator==(const Vector3& rhs) const; // exact compare, no epsilon
+ bool operator!=(const Vector3& rhs) const; // exact compare, no epsilon
+ bool operator<(const Vector3& rhs) const; // comparison for sort
+ float operator[](int index) const; // subscript operator v[0], v[1]
+ float& operator[](int index); // subscript operator v[0], v[1]
+
+ friend Vector3 operator*(const float a, const Vector3 vec);
+ friend std::ostream& operator<<(std::ostream& os, const Vector3& vec);
+};
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// 4D vector
+///////////////////////////////////////////////////////////////////////////////
+struct Vector4
+{
+ float x;
+ float y;
+ float z;
+ float w;
+
+ // ctors
+ Vector4() : x(0), y(0), z(0), w(0) {};
+ Vector4(float x, float y, float z, float w) : x(x), y(y), z(z), w(w) {};
+
+ // utils functions
+ void set(float x, float y, float z, float w);
+ float length() const; //
+ float distance(const Vector4& vec) const; // distance between two vectors
+ Vector4& normalize(); //
+ float dot(const Vector4& vec) const; // dot product
+ bool equal(const Vector4& vec, float e) const; // compare with epsilon
+
+ // operators
+ Vector4 operator-() const; // unary operator (negate)
+ Vector4 operator+(const Vector4& rhs) const; // add rhs
+ Vector4 operator-(const Vector4& rhs) const; // subtract rhs
+ Vector4& operator+=(const Vector4& rhs); // add rhs and update this object
+ Vector4& operator-=(const Vector4& rhs); // subtract rhs and update this object
+ Vector4 operator*(const float scale) const; // scale
+ Vector4 operator*(const Vector4& rhs) const; // multiply each element
+ Vector4& operator*=(const float scale); // scale and update this object
+ Vector4& operator*=(const Vector4& rhs); // multiply each element and update this object
+ Vector4 operator/(const float scale) const; // inverse scale
+ Vector4& operator/=(const float scale); // scale and update this object
+ bool operator==(const Vector4& rhs) const; // exact compare, no epsilon
+ bool operator!=(const Vector4& rhs) const; // exact compare, no epsilon
+ bool operator<(const Vector4& rhs) const; // comparison for sort
+ float operator[](int index) const; // subscript operator v[0], v[1]
+ float& operator[](int index); // subscript operator v[0], v[1]
+
+ friend Vector4 operator*(const float a, const Vector4 vec);
+ friend std::ostream& operator<<(std::ostream& os, const Vector4& vec);
+};
+
+
+
+// fast math routines from Doom3 SDK
+inline float invSqrt(float x)
+{
+ float xhalf = 0.5f * x;
+ int i = *(int*)&x; // get bits for floating value
+ i = 0x5f3759df - (i>>1); // gives initial guess
+ x = *(float*)&i; // convert bits back to float
+ x = x * (1.5f - xhalf*x*x); // Newton step
+ return x;
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inline functions for Vector2
+///////////////////////////////////////////////////////////////////////////////
+inline Vector2 Vector2::operator-() const {
+ return Vector2(-x, -y);
+}
+
+inline Vector2 Vector2::operator+(const Vector2& rhs) const {
+ return Vector2(x+rhs.x, y+rhs.y);
+}
+
+inline Vector2 Vector2::operator-(const Vector2& rhs) const {
+ return Vector2(x-rhs.x, y-rhs.y);
+}
+
+inline Vector2& Vector2::operator+=(const Vector2& rhs) {
+ x += rhs.x; y += rhs.y; return *this;
+}
+
+inline Vector2& Vector2::operator-=(const Vector2& rhs) {
+ x -= rhs.x; y -= rhs.y; return *this;
+}
+
+inline Vector2 Vector2::operator*(const float a) const {
+ return Vector2(x*a, y*a);
+}
+
+inline Vector2 Vector2::operator*(const Vector2& rhs) const {
+ return Vector2(x*rhs.x, y*rhs.y);
+}
+
+inline Vector2& Vector2::operator*=(const float a) {
+ x *= a; y *= a; return *this;
+}
+
+inline Vector2& Vector2::operator*=(const Vector2& rhs) {
+ x *= rhs.x; y *= rhs.y; return *this;
+}
+
+inline Vector2 Vector2::operator/(const float a) const {
+ return Vector2(x/a, y/a);
+}
+
+inline Vector2& Vector2::operator/=(const float a) {
+ x /= a; y /= a; return *this;
+}
+
+inline bool Vector2::operator==(const Vector2& rhs) const {
+ return (x == rhs.x) && (y == rhs.y);
+}
+
+inline bool Vector2::operator!=(const Vector2& rhs) const {
+ return (x != rhs.x) || (y != rhs.y);
+}
+
+inline bool Vector2::operator<(const Vector2& rhs) const {
+ if(x < rhs.x) return true;
+ if(x > rhs.x) return false;
+ if(y < rhs.y) return true;
+ if(y > rhs.y) return false;
+ return false;
+}
+
+inline float Vector2::operator[](int index) const {
+ return (&x)[index];
+}
+
+inline float& Vector2::operator[](int index) {
+ return (&x)[index];
+}
+
+inline void Vector2::set(float x_, float y_) {
+ this->x = x_; this->y = y_;
+}
+
+inline float Vector2::length() const {
+ return sqrtf(x*x + y*y);
+}
+
+inline float Vector2::distance(const Vector2& vec) const {
+ return sqrtf((vec.x-x)*(vec.x-x) + (vec.y-y)*(vec.y-y));
+}
+
+inline Vector2& Vector2::normalize() {
+ //@@const float EPSILON = 0.000001f;
+ float xxyy = x*x + y*y;
+ //@@if(xxyy < EPSILON)
+ //@@ return *this;
+
+ //float invLength = invSqrt(xxyy);
+ float invLength = 1.0f / sqrtf(xxyy);
+ x *= invLength;
+ y *= invLength;
+ return *this;
+}
+
+inline float Vector2::dot(const Vector2& rhs) const {
+ return (x*rhs.x + y*rhs.y);
+}
+
+inline bool Vector2::equal(const Vector2& rhs, float epsilon) const {
+ return fabs(x - rhs.x) < epsilon && fabs(y - rhs.y) < epsilon;
+}
+
+inline Vector2 operator*(const float a, const Vector2 vec) {
+ return Vector2(a*vec.x, a*vec.y);
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Vector2& vec) {
+ os << "(" << vec.x << ", " << vec.y << ")";
+ return os;
+}
+// END OF VECTOR2 /////////////////////////////////////////////////////////////
+
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inline functions for Vector3
+///////////////////////////////////////////////////////////////////////////////
+inline Vector3 Vector3::operator-() const {
+ return Vector3(-x, -y, -z);
+}
+
+inline Vector3 Vector3::operator+(const Vector3& rhs) const {
+ return Vector3(x+rhs.x, y+rhs.y, z+rhs.z);
+}
+
+inline Vector3 Vector3::operator-(const Vector3& rhs) const {
+ return Vector3(x-rhs.x, y-rhs.y, z-rhs.z);
+}
+
+inline Vector3& Vector3::operator+=(const Vector3& rhs) {
+ x += rhs.x; y += rhs.y; z += rhs.z; return *this;
+}
+
+inline Vector3& Vector3::operator-=(const Vector3& rhs) {
+ x -= rhs.x; y -= rhs.y; z -= rhs.z; return *this;
+}
+
+inline Vector3 Vector3::operator*(const float a) const {
+ return Vector3(x*a, y*a, z*a);
+}
+
+inline Vector3 Vector3::operator*(const Vector3& rhs) const {
+ return Vector3(x*rhs.x, y*rhs.y, z*rhs.z);
+}
+
+inline Vector3& Vector3::operator*=(const float a) {
+ x *= a; y *= a; z *= a; return *this;
+}
+
+inline Vector3& Vector3::operator*=(const Vector3& rhs) {
+ x *= rhs.x; y *= rhs.y; z *= rhs.z; return *this;
+}
+
+inline Vector3 Vector3::operator/(const float a) const {
+ return Vector3(x/a, y/a, z/a);
+}
+
+inline Vector3& Vector3::operator/=(const float a) {
+ x /= a; y /= a; z /= a; return *this;
+}
+
+inline bool Vector3::operator==(const Vector3& rhs) const {
+ return (x == rhs.x) && (y == rhs.y) && (z == rhs.z);
+}
+
+inline bool Vector3::operator!=(const Vector3& rhs) const {
+ return (x != rhs.x) || (y != rhs.y) || (z != rhs.z);
+}
+
+inline bool Vector3::operator<(const Vector3& rhs) const {
+ if(x < rhs.x) return true;
+ if(x > rhs.x) return false;
+ if(y < rhs.y) return true;
+ if(y > rhs.y) return false;
+ if(z < rhs.z) return true;
+ if(z > rhs.z) return false;
+ return false;
+}
+
+inline float Vector3::operator[](int index) const {
+ return (&x)[index];
+}
+
+inline float& Vector3::operator[](int index) {
+ return (&x)[index];
+}
+
+inline void Vector3::set(float x_, float y_, float z_) {
+ this->x = x_; this->y = y_; this->z = z_;
+}
+
+inline float Vector3::length() const {
+ return sqrtf(x*x + y*y + z*z);
+}
+
+inline float Vector3::distance(const Vector3& vec) const {
+ return sqrtf((vec.x-x)*(vec.x-x) + (vec.y-y)*(vec.y-y) + (vec.z-z)*(vec.z-z));
+}
+
+inline Vector3& Vector3::normalize() {
+ //@@const float EPSILON = 0.000001f;
+ float xxyyzz = x*x + y*y + z*z;
+ //@@if(xxyyzz < EPSILON)
+ //@@ return *this; // do nothing if it is ~zero vector
+
+ //float invLength = invSqrt(xxyyzz);
+ float invLength = 1.0f / sqrtf(xxyyzz);
+ x *= invLength;
+ y *= invLength;
+ z *= invLength;
+ return *this;
+}
+
+inline float Vector3::dot(const Vector3& rhs) const {
+ return (x*rhs.x + y*rhs.y + z*rhs.z);
+}
+
+inline Vector3 Vector3::cross(const Vector3& rhs) const {
+ return Vector3(y*rhs.z - z*rhs.y, z*rhs.x - x*rhs.z, x*rhs.y - y*rhs.x);
+}
+
+inline bool Vector3::equal(const Vector3& rhs, float epsilon) const {
+ return fabs(x - rhs.x) < epsilon && fabs(y - rhs.y) < epsilon && fabs(z - rhs.z) < epsilon;
+}
+
+inline Vector3 operator*(const float a, const Vector3 vec) {
+ return Vector3(a*vec.x, a*vec.y, a*vec.z);
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Vector3& vec) {
+ os << "(" << vec.x << ", " << vec.y << ", " << vec.z << ")";
+ return os;
+}
+// END OF VECTOR3 /////////////////////////////////////////////////////////////
+
+
+
+///////////////////////////////////////////////////////////////////////////////
+// inline functions for Vector4
+///////////////////////////////////////////////////////////////////////////////
+inline Vector4 Vector4::operator-() const {
+ return Vector4(-x, -y, -z, -w);
+}
+
+inline Vector4 Vector4::operator+(const Vector4& rhs) const {
+ return Vector4(x+rhs.x, y+rhs.y, z+rhs.z, w+rhs.w);
+}
+
+inline Vector4 Vector4::operator-(const Vector4& rhs) const {
+ return Vector4(x-rhs.x, y-rhs.y, z-rhs.z, w-rhs.w);
+}
+
+inline Vector4& Vector4::operator+=(const Vector4& rhs) {
+ x += rhs.x; y += rhs.y; z += rhs.z; w += rhs.w; return *this;
+}
+
+inline Vector4& Vector4::operator-=(const Vector4& rhs) {
+ x -= rhs.x; y -= rhs.y; z -= rhs.z; w -= rhs.w; return *this;
+}
+
+inline Vector4 Vector4::operator*(const float a) const {
+ return Vector4(x*a, y*a, z*a, w*a);
+}
+
+inline Vector4 Vector4::operator*(const Vector4& rhs) const {
+ return Vector4(x*rhs.x, y*rhs.y, z*rhs.z, w*rhs.w);
+}
+
+inline Vector4& Vector4::operator*=(const float a) {
+ x *= a; y *= a; z *= a; w *= a; return *this;
+}
+
+inline Vector4& Vector4::operator*=(const Vector4& rhs) {
+ x *= rhs.x; y *= rhs.y; z *= rhs.z; w *= rhs.w; return *this;
+}
+
+inline Vector4 Vector4::operator/(const float a) const {
+ return Vector4(x/a, y/a, z/a, w/a);
+}
+
+inline Vector4& Vector4::operator/=(const float a) {
+ x /= a; y /= a; z /= a; w /= a; return *this;
+}
+
+inline bool Vector4::operator==(const Vector4& rhs) const {
+ return (x == rhs.x) && (y == rhs.y) && (z == rhs.z) && (w == rhs.w);
+}
+
+inline bool Vector4::operator!=(const Vector4& rhs) const {
+ return (x != rhs.x) || (y != rhs.y) || (z != rhs.z) || (w != rhs.w);
+}
+
+inline bool Vector4::operator<(const Vector4& rhs) const {
+ if(x < rhs.x) return true;
+ if(x > rhs.x) return false;
+ if(y < rhs.y) return true;
+ if(y > rhs.y) return false;
+ if(z < rhs.z) return true;
+ if(z > rhs.z) return false;
+ if(w < rhs.w) return true;
+ if(w > rhs.w) return false;
+ return false;
+}
+
+inline float Vector4::operator[](int index) const {
+ return (&x)[index];
+}
+
+inline float& Vector4::operator[](int index) {
+ return (&x)[index];
+}
+
+inline void Vector4::set(float x_, float y_, float z_, float w_) {
+ this->x = x_; this->y = y_; this->z = z_; this->w = w_;
+}
+
+inline float Vector4::length() const {
+ return sqrtf(x*x + y*y + z*z + w*w);
+}
+
+inline float Vector4::distance(const Vector4& vec) const {
+ return sqrtf((vec.x-x)*(vec.x-x) + (vec.y-y)*(vec.y-y) + (vec.z-z)*(vec.z-z) + (vec.w-w)*(vec.w-w));
+}
+
+inline Vector4& Vector4::normalize() {
+ //NOTE: leave w-component untouched
+ //@@const float EPSILON = 0.000001f;
+ float xxyyzz = x*x + y*y + z*z;
+ //@@if(xxyyzz < EPSILON)
+ //@@ return *this; // do nothing if it is zero vector
+
+ //float invLength = invSqrt(xxyyzz);
+ float invLength = 1.0f / sqrtf(xxyyzz);
+ x *= invLength;
+ y *= invLength;
+ z *= invLength;
+ return *this;
+}
+
+inline float Vector4::dot(const Vector4& rhs) const {
+ return (x*rhs.x + y*rhs.y + z*rhs.z + w*rhs.w);
+}
+
+inline bool Vector4::equal(const Vector4& rhs, float epsilon) const {
+ return fabs(x - rhs.x) < epsilon && fabs(y - rhs.y) < epsilon &&
+ fabs(z - rhs.z) < epsilon && fabs(w - rhs.w) < epsilon;
+}
+
+inline Vector4 operator*(const float a, const Vector4 vec) {
+ return Vector4(a*vec.x, a*vec.y, a*vec.z, a*vec.w);
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Vector4& vec) {
+ os << "(" << vec.x << ", " << vec.y << ", " << vec.z << ", " << vec.w << ")";
+ return os;
+}
+// END OF VECTOR4 /////////////////////////////////////////////////////////////
+
+#endif
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-22 06:27:22 +0000