/*
** Command & Conquer Generals(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 <http://www.gnu.org/licenses/>.
*/
/* $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 <math.h>
#include <assert.h>
#include <stdlib.h>
//#include <stdio.h>
#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);
}