/* ** Command & Conquer Renegade(tm) ** Copyright 2025 Electronic Arts Inc. ** ** This program is free software: you can redistribute it and/or modify ** it under the terms of the GNU General Public License as published by ** the Free Software Foundation, either version 3 of the License, or ** (at your option) any later version. ** ** This program is distributed in the hope that it will be useful, ** but WITHOUT ANY WARRANTY; without even the implied warranty of ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ** GNU General Public License for more details. ** ** You should have received a copy of the GNU General Public License ** along with this program. If not, see . */ /* $Header: /Commando/Code/Tools/max2w3d/matrix3d.cpp 39 2/03/00 4:55p Jason_a $ */ /*********************************************************************************************** *** Confidential - Westwood Studios *** *********************************************************************************************** * * * Project Name : Voxel Technology * * * * File Name : MATRIX3D.CPP * * * * Programmer : Greg Hjelstrom * * * * Start Date : 02/24/97 * * * * Last Update : February 28, 1997 [GH] * * * *---------------------------------------------------------------------------------------------* * Functions: * * Matrix3D::Set_Rotation -- Sets the rotation part of the matrix * * Matrix3D::Set_Rotation -- Sets the rotation part of the matrix * * Matrix3D::Set -- Init a matrix3D from a matrix3 and a position * * Matrix3D::Set -- Init a matrix3D from a quaternion and a position * * Matrix3D::Get_X_Rotation -- approximates the rotation about the X axis * * Matrix3D::Get_Y_Rotation -- approximates the rotation about the Y axis * * Matrix3D::Get_Z_Rotation -- approximates the rotation about the Z axis * * Matrix3D::Multiply -- matrix multiplication without temporaries. * * Matrix3D::Inverse_Rotate_Vector -- rotates a vector by the inverse of the 3x3 sub-matrix * * Matrix3D::Transform_Min_Max_AABox -- compute transformed axis-aligned box * * Matrix3D::Transform_Center_Extent_AABox -- compute transformed axis-aligned box * * Matrix3D::Get_Inverse -- calculate the inverse of this matrix * * Matrix3D::Get_Orthogonal_Inverse -- Returns the inverse of the matrix * * Matrix3D::Re_Orthogonalize -- makes this matrix orthogonal. * * Matrix3D::Is_Orthogonal -- checks whether this matrix is orthogonal * * Lerp - linearly interpolate matrices (orientation is slerped) * * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ #include "matrix3d.h" #include #include #include //#include #include "vector3.h" #include "wwmatrix3.h" #include "matrix4.h" #include "w3dquat.h" // some static matrices which are sometimes useful const Matrix3D Matrix3D::Identity ( 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ); const Matrix3D Matrix3D::RotateX90 ( 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, 0.0, 0.0 ); const Matrix3D Matrix3D::RotateX180 ( 1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0 ); const Matrix3D Matrix3D::RotateX270 ( 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0, 0.0 ); const Matrix3D Matrix3D::RotateY90 ( 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0 ); const Matrix3D Matrix3D::RotateY180 ( -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0 ); const Matrix3D Matrix3D::RotateY270 ( 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0 ); const Matrix3D Matrix3D::RotateZ90 ( 0.0, -1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ); const Matrix3D Matrix3D::RotateZ180 ( -1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ); const Matrix3D Matrix3D::RotateZ270 ( 0.0, 1.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ); /*********************************************************************************************** * Matrix3D::Set -- Init a matrix3D from a matrix3 and a position * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * *=============================================================================================*/ void Matrix3D::Set(const Matrix3 & rot,const Vector3 & pos) { Row[0].Set( rot[0][0], rot[0][1], rot[0][2], pos[0]); Row[1].Set( rot[1][0], rot[1][1], rot[1][2], pos[1]); Row[2].Set( rot[2][0], rot[2][1], rot[2][2], pos[2]); } /*********************************************************************************************** * Matrix3D::Set -- Init a matrix3D from a quaternion and a position * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * *=============================================================================================*/ void Matrix3D::Set(const Quaternion & rot,const Vector3 & pos) { Set_Rotation(rot); Set_Translation(pos); } /*********************************************************************************************** * Matrix3D::Set_Rotation -- Sets the rotation part of the matrix * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 5/11/98 GTH : Created. * *=============================================================================================*/ void Matrix3D::Set_Rotation(const Matrix3 & m) { Row[0][0] = m[0][0]; Row[0][1] = m[0][1]; Row[0][2] = m[0][2]; Row[1][0] = m[1][0]; Row[1][1] = m[1][1]; Row[1][2] = m[1][2]; Row[2][0] = m[2][0]; Row[2][1] = m[2][1]; Row[2][2] = m[2][2]; } /*********************************************************************************************** * Matrix3D::Set_Rotation -- Sets the rotation part of the matrix * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 5/11/98 GTH : Created. * *=============================================================================================*/ void Matrix3D::Set_Rotation(const Quaternion & q) { Row[0][0] = (float)(1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2])); Row[0][1] = (float)(2.0 * (q[0] * q[1] - q[2] * q[3])); Row[0][2] = (float)(2.0 * (q[2] * q[0] + q[1] * q[3])); Row[1][0] = (float)(2.0 * (q[0] * q[1] + q[2] * q[3])); Row[1][1] = (float)(1.0 - 2.0f * (q[2] * q[2] + q[0] * q[0])); Row[1][2] = (float)(2.0 * (q[1] * q[2] - q[0] * q[3])); Row[2][0] = (float)(2.0 * (q[2] * q[0] - q[1] * q[3])); Row[2][1] = (float)(2.0 * (q[1] * q[2] + q[0] * q[3])); Row[2][2] =(float)(1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0])); } /*********************************************************************************************** * Matrix3D::Get_X_Rotation -- approximates the rotation about the X axis * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 08/11/1997 GH : Created. * *=============================================================================================*/ float Matrix3D::Get_X_Rotation(void) const { return atan2(Row[2][1], Row[1][1]); } /*********************************************************************************************** * Matrix3D::Get_Y_Rotation -- approximates the rotation about the Y axis * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 08/11/1997 GH : Created. * *=============================================================================================*/ float Matrix3D::Get_Y_Rotation(void) const { return atan2(Row[0][2], Row[2][2]); } /*********************************************************************************************** * Matrix3D::Get_Z_Rotation -- approximates the rotation about the Z axis * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 08/11/1997 GH : Created. * *=============================================================================================*/ float Matrix3D::Get_Z_Rotation(void) const { return atan2(Row[1][0], Row[0][0]); } /*********************************************************************************************** * M3DC::Rotate_Vector -- Uses the 3x3 sub-matrix to rotate a vector * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * *=============================================================================================*/ Vector3 Matrix3D::Rotate_Vector(const Vector3 &vect) const { return Vector3( (Row[0][0]*vect[0] + Row[0][1]*vect[1] + Row[0][2]*vect[2]), (Row[1][0]*vect[0] + Row[1][1]*vect[1] + Row[1][2]*vect[2]), (Row[2][0]*vect[0] + Row[2][1]*vect[1] + Row[2][2]*vect[2]) ); } /*********************************************************************************************** * Matrix3D::Inverse_Rotate_Vector -- rotates a vector by the inverse of the 3x3 sub-matrix * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 4/27/98 GTH : Created. * *=============================================================================================*/ Vector3 Matrix3D::Inverse_Rotate_Vector(const Vector3 &vect) const { return Vector3( (Row[0][0]*vect[0] + Row[1][0]*vect[1] + Row[2][0]*vect[2]), (Row[0][1]*vect[0] + Row[1][1]*vect[1] + Row[2][1]*vect[2]), (Row[0][2]*vect[0] + Row[1][2]*vect[1] + Row[2][2]*vect[2]) ); } /*********************************************************************************************** * M3DC::Look_At -- Creates a "look at" transformation. * * * * Builds a transformation matrix which positions the origin at p, * * points the negative z-axis towards a target t, and rolls about the z-axis * * by the angle specified by roll. * * * * This can be useful for creating a camera matrix, just invert * * the matrix after initializing it with this function... * * * * INPUT: * * p - position of the coordinate system * * t - target of the coordinate system * * roll - roll angle (in radians) * * * * OUTPUT: * * * * WARNINGS: * * This function is written assuming the convention that the "ground" is the X-Y plane and * * Z is altitude. * * * * HISTORY: * *=============================================================================================*/ void Matrix3D::Look_At(const Vector3 &p,const Vector3 &t,float roll) { float dx,dy,dz; //vector from p to t float len1,len2; float sinp,cosp; //sine and cosine of the pitch ("up-down" tilt about x) float siny,cosy; //sine and cosine of the yaw ("left-right"tilt about z) dx = (t[0] - p[0]); dy = (t[1] - p[1]); dz = (t[2] - p[2]); len1 = (float)WWMath::Sqrt(dx*dx + dy*dy + dz*dz); len2 = (float)WWMath::Sqrt(dx*dx + dy*dy); if (len1 != 0.0f) { sinp = dz/len1; cosp = len2/len1; } else { sinp = 0.0f; cosp = 1.0f; } if (len2 != 0.0f) { siny = dy/len2; cosy = dx/len2; } else { siny = 0.0f; cosy = 1.0f; } // init the matrix with position p and -z pointing down +x and +y up Row[0].X = 0.0f; Row[0].Y = 0.0f; Row[0].Z = -1.0f; Row[1].X = -1.0f; Row[1].Y = 0.0f; Row[1].Z = 0.0f; Row[2].X = 0.0f; Row[2].Y = 1.0f; Row[2].Z = 0.0f; Row[0].W = p.X; Row[1].W = p.Y; Row[2].W = p.Z; // Yaw rotation to make the matrix look at the projection of the target // into the x-y plane Rotate_Y(siny,cosy); // rotate about local x axis to pitch up to the targets position Rotate_X(sinp,cosp); // roll about the local z axis (negate since we look down -z) Rotate_Z(-roll); } /*********************************************************************************************** * M3DC::Obj_Look_At -- Commando Object "look at" transformation. * * * * Builds a transformation matrix which positions the origin at p, * * points the positive X axis towards a target t, and rolls about the X axis * * by the angle specified by roll. * * * * The object convention used by Commando and G is Forward = +X, Left = +Y, Up = +Z. The * * world is basically the x-y plane with z as altitude and +x is the default "forward". * * * * INPUT: * * p - position of the coordinate system * * t - target of the coordinate system * * roll - roll angle (in radians) * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * *=============================================================================================*/ void Matrix3D::Obj_Look_At(const Vector3 &p,const Vector3 &t,float roll) { float dx,dy,dz; //vector from p to t float len1,len2; float sinp,cosp; //sine and cosine of the pitch ("up-down" tilt about y) float siny,cosy; //sine and cosine of the yaw ("left-right"tilt about z) dx = (t[0] - p[0]); dy = (t[1] - p[1]); dz = (t[2] - p[2]); len1 = (float)sqrt(dx*dx + dy*dy + dz*dz); len2 = (float)sqrt(dx*dx + dy*dy); if (len1 != 0.0f) { sinp = dz/len1; cosp = len2/len1; } else { sinp = 0.0f; cosp = 1.0f; } if (len2 != 0.0f) { siny = dy/len2; cosy = dx/len2; } else { siny = 0.0f; cosy = 1.0f; } Make_Identity(); Translate(p); // Yaw rotation to projection of target in x-y plane Rotate_Z(siny,cosy); // Pitch rotation Rotate_Y(-sinp,cosp); // Roll rotation Rotate_X(roll); } /*********************************************************************************************** * Matrix3D::Get_Inverse -- calculate the inverse of this matrix * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 8/7/98 GTH : Created. * *=============================================================================================*/ void Matrix3D::Get_Inverse(Matrix3D & inv) const { // TODO: Implement the general purpose inverse function here (once we need it :-) Get_Orthogonal_Inverse(inv); } /*********************************************************************************************** * Matrix3D::Get_Orthogonal_Inverse -- Returns the inverse of the matrix * * * * NOTE!!! This only works if the matrix is really ORTHOGONAL!!! * * * *********************************************************************************************** * Inverting an orthogonal Matrix3D * * * * M is the original transform, * * R is rotation submatrix, * * T is translation vector in M. * * * * To build MINV * * * * R' = transpose of R (inverse of orthogonal 3x3 matrix is transpose) * * T' = -R'T * * * * Build MINV with R'and T' * * MINV is the inverse of M * * * *********************************************************************************************** * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * *=============================================================================================*/ void Matrix3D::Get_Orthogonal_Inverse(Matrix3D & inv) const { // Transposing the rotation submatrix inv.Row[0][0] = Row[0][0]; inv.Row[0][1] = Row[1][0]; inv.Row[0][2] = Row[2][0]; inv.Row[1][0] = Row[0][1]; inv.Row[1][1] = Row[1][1]; inv.Row[1][2] = Row[2][1]; inv.Row[2][0] = Row[0][2]; inv.Row[2][1] = Row[1][2]; inv.Row[2][2] = Row[2][2]; // Now, calculate translation portion of matrix: // T' = -R'T Vector3 trans = Get_Translation(); trans = inv.Rotate_Vector(trans); trans = -trans; inv.Row[0][3] = trans[0]; inv.Row[1][3] = trans[1]; inv.Row[2][3] = trans[2]; } /*********************************************************************************************** * Copy_3x3_Matrix(float *matrix) -- Copies a 3x3 (float[9]) matrix into this matrix * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 1/16/98 EHC : Created. * *=============================================================================================*/ void Matrix3D::Copy_3x3_Matrix(float matrix[3][3]) { Row[0][0] = matrix[0][0]; Row[0][1] = matrix[0][1]; Row[0][2] = matrix[0][2]; Row[0][3] = 0; Row[1][0] = matrix[1][0]; Row[1][1] = matrix[1][1]; Row[1][2] = matrix[1][2]; Row[1][3] = 0; Row[2][0] = matrix[2][0]; Row[2][1] = matrix[2][1]; Row[2][2] = matrix[2][2]; Row[2][3] = 0; } /*********************************************************************************************** * Matrix3D::Multiply -- matrix multiplication without temporaries. * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 4/22/98 GTH : Created. * *=============================================================================================*/ //void print_matrix(const Matrix3D & m); void Matrix3D::Multiply(const Matrix3D & A,const Matrix3D & B,Matrix3D * set_res) { assert(set_res != NULL); Matrix3D tmp; Matrix3D * Aptr; float tmp1,tmp2,tmp3; // Check for aliased parameters, copy the 'A' matrix into a temporary if the // result is going into 'A'. (in this case, this function is no better than // the overloaded C++ operator...) if (set_res == &A) { tmp = A; Aptr = &tmp; } else { Aptr = (Matrix3D *)&A; } tmp1 = B[0][0]; tmp2 = B[1][0]; tmp3 = B[2][0]; (*set_res)[0][0] = (*Aptr)[0][0]*tmp1 + (*Aptr)[0][1]*tmp2 + (*Aptr)[0][2]*tmp3; (*set_res)[1][0] = (*Aptr)[1][0]*tmp1 + (*Aptr)[1][1]*tmp2 + (*Aptr)[1][2]*tmp3; (*set_res)[2][0] = (*Aptr)[2][0]*tmp1 + (*Aptr)[2][1]*tmp2 + (*Aptr)[2][2]*tmp3; tmp1 = B[0][1]; tmp2 = B[1][1]; tmp3 = B[2][1]; (*set_res)[0][1] = (*Aptr)[0][0]*tmp1 + (*Aptr)[0][1]*tmp2 + (*Aptr)[0][2]*tmp3; (*set_res)[1][1] = (*Aptr)[1][0]*tmp1 + (*Aptr)[1][1]*tmp2 + (*Aptr)[1][2]*tmp3; (*set_res)[2][1] = (*Aptr)[2][0]*tmp1 + (*Aptr)[2][1]*tmp2 + (*Aptr)[2][2]*tmp3; tmp1 = B[0][2]; tmp2 = B[1][2]; tmp3 = B[2][2]; (*set_res)[0][2] = (*Aptr)[0][0]*tmp1 + (*Aptr)[0][1]*tmp2 + (*Aptr)[0][2]*tmp3; (*set_res)[1][2] = (*Aptr)[1][0]*tmp1 + (*Aptr)[1][1]*tmp2 + (*Aptr)[1][2]*tmp3; (*set_res)[2][2] = (*Aptr)[2][0]*tmp1 + (*Aptr)[2][1]*tmp2 + (*Aptr)[2][2]*tmp3; tmp1 = B[0][3]; tmp2 = B[1][3]; tmp3 = B[2][3]; (*set_res)[0][3] = (*Aptr)[0][0]*tmp1 + (*Aptr)[0][1]*tmp2 + (*Aptr)[0][2]*tmp3 + (*Aptr)[0][3]; (*set_res)[1][3] = (*Aptr)[1][0]*tmp1 + (*Aptr)[1][1]*tmp2 + (*Aptr)[1][2]*tmp3 + (*Aptr)[1][3]; (*set_res)[2][3] = (*Aptr)[2][0]*tmp1 + (*Aptr)[2][1]*tmp2 + (*Aptr)[2][2]*tmp3 + (*Aptr)[2][3]; } /*********************************************************************************************** * Matrix3D::Transform_Min_Max_AABox -- compute transformed axis-aligned box * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 7/17/98 GTH : Created. * *=============================================================================================*/ void Matrix3D::Transform_Min_Max_AABox ( const Vector3 & min, const Vector3 & max, Vector3 * set_min, Vector3 * set_max ) const { assert(set_min != &min); assert(set_max != &max); float tmp0,tmp1; // init the min and max to the translation of the transform set_min->X = set_max->X = Row[0][3]; set_min->Y = set_max->Y = Row[1][3]; set_min->Z = set_max->Z = Row[2][3]; // now push them both out by the projections of the original intervals for (int i=0; i<3; i++) { for (int j=0; j<3; j++) { tmp0 = Row[i][j] * min[j]; tmp1 = Row[i][j] * max[j]; if (tmp0 < tmp1) { (*set_min)[i] += tmp0; (*set_max)[i] += tmp1; } else { (*set_min)[i] += tmp1; (*set_max)[i] += tmp0; } } } } /*********************************************************************************************** * Matrix3D::Transform_Center_Extent_AABox -- compute transformed axis-aligned box * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 7/17/98 GTH : Created. * *=============================================================================================*/ void Matrix3D::Transform_Center_Extent_AABox ( const Vector3 & center, const Vector3 & extent, Vector3 * set_center, Vector3 * set_extent ) const { assert(set_center != ¢er); assert(set_extent != &extent); // push each extent out to the projections of the original extents for (int i=0; i<3; i++) { // start the center out at the translation portion of the matrix // and the extent at zero (*set_center)[i] = Row[i][3]; (*set_extent)[i] = 0.0f; for (int j=0; j<3; j++) { (*set_center)[i] += Row[i][j] * center[j]; (*set_extent)[i] += WWMath::Fabs(Row[i][j] * extent[j]); } } } /*********************************************************************************************** * Matrix3D::Is_Orthogonal -- checks whether this matrix is orthogonal * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 9/16/98 GTH : Created. * *=============================================================================================*/ int Matrix3D::Is_Orthogonal(void) const { Vector3 x(Row[0].X,Row[0].Y,Row[0].Z); Vector3 y(Row[1].X,Row[1].Y,Row[1].Z); Vector3 z(Row[2].X,Row[2].Y,Row[2].Z); if (Vector3::Dot_Product(x,y) > WWMATH_EPSILON) return 0; if (Vector3::Dot_Product(y,z) > WWMATH_EPSILON) return 0; if (Vector3::Dot_Product(z,x) > WWMATH_EPSILON) return 0; if (WWMath::Fabs(x.Length() - 1.0f) > WWMATH_EPSILON) return 0; if (WWMath::Fabs(y.Length() - 1.0f) > WWMATH_EPSILON) return 0; if (WWMath::Fabs(z.Length() - 1.0f) > WWMATH_EPSILON) return 0; return 1; } /*********************************************************************************************** * Matrix3D::Re_Orthogonalize -- makes this matrix orthogonal. * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * This function is rather expensive, should only be used if you *know* numerical error is * * killing you. * * * * HISTORY: * * 9/16/98 GTH : Created. * *=============================================================================================*/ void Matrix3D::Re_Orthogonalize(void) { Vector3 x(Row[0][0],Row[0][1],Row[0][2]); Vector3 y(Row[1][0],Row[1][1],Row[1][2]); Vector3 z; Vector3::Cross_Product(x,y,&z); Vector3::Cross_Product(z,x,&y); float len = x.Length(); if (len < WWMATH_EPSILON) { Make_Identity(); return; } else { x *= 1.0f/len; } len = y.Length(); if (len < WWMATH_EPSILON) { Make_Identity(); return; } else { y *= 1.0f/len; } len = z.Length(); if (len < WWMATH_EPSILON) { Make_Identity(); return; } else { z *= 1.0f/len; } Row[0][0] = x.X; Row[0][1] = x.Y; Row[0][2] = x.Z; Row[1][0] = y.X; Row[1][1] = y.Y; Row[1][2] = y.Z; Row[2][0] = z.X; Row[2][1] = z.Y; Row[2][2] = z.Z; } /*********************************************************************************************** * Lerp - linearly interpolate matrices (orientation is slerped) * * * * INPUT: * * * * OUTPUT: * * * * WARNINGS: * * * * HISTORY: * * 10/05/1998 NH : Created. * *=============================================================================================*/ Matrix3D Lerp(const Matrix3D &A, const Matrix3D &B, float factor) { assert(factor >= 0.0f); assert(factor <= 1.0f); // Lerp position Vector3 pos = Lerp(A.Get_Translation(), B.Get_Translation(), factor); Quaternion rot = Slerp(Build_Quaternion(A), Build_Quaternion(B), factor); return Matrix3D(rot, pos); }