godot/core/math/camera_matrix.cpp

/*************************************************************************/
/*  camera_matrix.cpp                                                    */
/*************************************************************************/
/*                       This file is part of:                           */
/*                           GODOT ENGINE                                */
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
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#include "camera_matrix.h"
#include "math_funcs.h"
#include "print_string.h"

void CameraMatrix::set_identity() {

	for (int i=0;i<4;i++) {

		for (int j=0;j<4;j++) {

			matrix[i][j]=(i==j)?1:0;
		}
	}
}


void CameraMatrix::set_zero() {

	for (int i=0;i<4;i++) {

		for (int j=0;j<4;j++) {

			matrix[i][j]=0;
		}
	}
}


Plane CameraMatrix::xform4(const Plane& p_vec4) const {

	Plane ret;

	ret.normal.x = matrix[0][0] * p_vec4.normal.x + matrix[1][0] * p_vec4.normal.y + matrix[2][0] * p_vec4.normal.z + matrix[3][0] * p_vec4.d;
	ret.normal.y = matrix[0][1] * p_vec4.normal.x + matrix[1][1] * p_vec4.normal.y + matrix[2][1] * p_vec4.normal.z + matrix[3][1] * p_vec4.d;
	ret.normal.z = matrix[0][2] * p_vec4.normal.x + matrix[1][2] * p_vec4.normal.y + matrix[2][2] * p_vec4.normal.z + matrix[3][2] * p_vec4.d;
	ret.d = matrix[0][3] * p_vec4.normal.x + matrix[1][3] * p_vec4.normal.y + matrix[2][3] * p_vec4.normal.z + matrix[3][3] * p_vec4.d;
	return ret;
}

void CameraMatrix::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far,bool p_flip_fov) {

	if (p_flip_fov) {
		p_fovy_degrees=get_fovy(p_fovy_degrees,1.0/p_aspect);

	}

	real_t sine, cotangent, deltaZ;
	real_t radians = p_fovy_degrees / 2.0 * Math_PI / 180.0;

	deltaZ = p_z_far - p_z_near;
	sine = Math::sin(radians);

		if ((deltaZ == 0) || (sine == 0) || (p_aspect == 0)) {
		return ;
	}
	cotangent = Math::cos(radians) / sine;

	set_identity();

	matrix[0][0] = cotangent / p_aspect;
	matrix[1][1] = cotangent;
	matrix[2][2] = -(p_z_far + p_z_near) / deltaZ;
	matrix[2][3] = -1;
	matrix[3][2] = -2 * p_z_near * p_z_far / deltaZ;
	matrix[3][3] = 0;

}

void CameraMatrix::set_orthogonal(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top,  real_t p_znear, real_t p_zfar) {


	set_identity();

	matrix[0][0] = 2.0/(p_right-p_left);
	matrix[3][0] = -((p_right+p_left)/(p_right-p_left));
	matrix[1][1] = 2.0/(p_top-p_bottom);
	matrix[3][1] = -((p_top+p_bottom)/(p_top-p_bottom));
	matrix[2][2] = -2.0/(p_zfar-p_znear);
	matrix[3][2] = -((p_zfar+p_znear)/(p_zfar-p_znear));
	matrix[3][3] = 1.0;

}

void CameraMatrix::set_orthogonal(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar,bool p_flip_fov) {

	if (!p_flip_fov) {
		p_size*=p_aspect;
	}

	set_orthogonal(-p_size/2,+p_size/2,-p_size/p_aspect/2,+p_size/p_aspect/2,p_znear,p_zfar);
}



void CameraMatrix::set_frustum(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far) {
#if 0
	///@TODO, give a check to this. I'm not sure if it's working.
	set_identity();

	matrix[0][0]=(2*p_near) / (p_right-p_left);
	matrix[0][2]=(p_right+p_left) / (p_right-p_left);
	matrix[1][1]=(2*p_near) / (p_top-p_bottom);
	matrix[1][2]=(p_top+p_bottom) / (p_top-p_bottom);
	matrix[2][2]=-(p_far+p_near) / ( p_far-p_near);
	matrix[2][3]=-(2*p_far*p_near) / (p_far-p_near);
	matrix[3][2]=-1;
	matrix[3][3]=0;
#else
	real_t *te = &matrix[0][0];
	real_t x = 2 * p_near / ( p_right - p_left );
	real_t y = 2 * p_near / ( p_top - p_bottom );

	real_t a = ( p_right + p_left ) / ( p_right - p_left );
	real_t b = ( p_top + p_bottom ) / ( p_top - p_bottom );
	real_t c = - ( p_far + p_near ) / ( p_far - p_near );
	real_t d = - 2 * p_far * p_near / ( p_far - p_near );

	te[0] = x;
	te[1] = 0;
	te[2] = 0;
	te[3] = 0;
	te[4] = 0;
	te[5] = y;
	te[6] = 0;
	te[7] = 0;
	te[8] = a;
	te[9] = b;
	te[10] = c;
	te[11] = -1;
	te[12] = 0;
	te[13] = 0;
	te[14] = d;
	te[15] = 0;

#endif

}



real_t CameraMatrix::get_z_far() const {

	const real_t * matrix = (const real_t*)this->matrix;
	Plane new_plane=Plane(matrix[ 3] - matrix[ 2],
	                matrix[ 7] - matrix[ 6],
	                matrix[11] - matrix[10],
	                matrix[15] - matrix[14]);

	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	return new_plane.d;
}
real_t CameraMatrix::get_z_near() const {

	const real_t * matrix = (const real_t*)this->matrix;
	Plane new_plane=Plane(matrix[ 3] + matrix[ 2],
	                matrix[ 7] + matrix[ 6],
	                matrix[11] + matrix[10],
	               -matrix[15] - matrix[14]);

	new_plane.normalize();
	return new_plane.d;
}

void CameraMatrix::get_viewport_size(real_t& r_width, real_t& r_height) const {

	const real_t * matrix = (const real_t*)this->matrix;
	///////--- Near Plane ---///////
	Plane near_plane=Plane(matrix[ 3] + matrix[ 2],
	                matrix[ 7] + matrix[ 6],
	                matrix[11] + matrix[10],
			-matrix[15] - matrix[14]);
	near_plane.normalize();

	///////--- Right Plane ---///////
	Plane right_plane=Plane(matrix[ 3] - matrix[ 0],
	                matrix[ 7] - matrix[ 4],
	                matrix[11] - matrix[ 8],
			- matrix[15] + matrix[12]);
	right_plane.normalize();

	Plane top_plane=Plane(matrix[ 3] - matrix[ 1],
	                matrix[ 7] - matrix[ 5],
	                matrix[11] - matrix[ 9],
			-matrix[15] + matrix[13]);
	top_plane.normalize();

	Vector3 res;
	near_plane.intersect_3(right_plane,top_plane,&res);

	r_width=res.x;
	r_height=res.y;
}

bool CameraMatrix::get_endpoints(const Transform& p_transform, Vector3 *p_8points) const {

	const real_t * matrix = (const real_t*)this->matrix;

	///////--- Near Plane ---///////
	Plane near_plane=Plane(matrix[ 3] + matrix[ 2],
	                matrix[ 7] + matrix[ 6],
	                matrix[11] + matrix[10],
			-matrix[15] - matrix[14]);
	near_plane.normalize();

	///////--- Far Plane ---///////
	Plane far_plane=Plane(matrix[ 2] - matrix[ 3],
		      matrix[ 6] - matrix[ 7],
		      matrix[10] - matrix[11],
		      matrix[15] - matrix[14]);
	far_plane.normalize();

	///////--- Right Plane ---///////
	Plane right_plane=Plane(matrix[ 0] - matrix[ 3],
	                matrix[ 4] - matrix[ 7],
	                matrix[8] - matrix[ 11],
			- matrix[15] + matrix[12]);
	right_plane.normalize();

	///////--- Top Plane ---///////
	Plane top_plane=Plane(matrix[ 1] - matrix[ 3],
	                matrix[ 5] - matrix[ 7],
	                matrix[9] - matrix[ 11],
			-matrix[15] + matrix[13]);
	top_plane.normalize();

	Vector3 near_endpoint;
	Vector3 far_endpoint;

	bool res=near_plane.intersect_3(right_plane,top_plane,&near_endpoint);
	ERR_FAIL_COND_V(!res,false);

	res=far_plane.intersect_3(right_plane,top_plane,&far_endpoint);
	ERR_FAIL_COND_V(!res,false);

	p_8points[0]=p_transform.xform( Vector3( near_endpoint.x, near_endpoint.y, near_endpoint.z ) );
	p_8points[1]=p_transform.xform( Vector3( near_endpoint.x,-near_endpoint.y, near_endpoint.z ) );
	p_8points[2]=p_transform.xform( Vector3(-near_endpoint.x, near_endpoint.y, near_endpoint.z ) );
	p_8points[3]=p_transform.xform( Vector3(-near_endpoint.x,-near_endpoint.y, near_endpoint.z ) );
	p_8points[4]=p_transform.xform( Vector3( far_endpoint.x, far_endpoint.y, far_endpoint.z ) );
	p_8points[5]=p_transform.xform( Vector3( far_endpoint.x,-far_endpoint.y, far_endpoint.z ) );
	p_8points[6]=p_transform.xform( Vector3(-far_endpoint.x, far_endpoint.y, far_endpoint.z ) );
	p_8points[7]=p_transform.xform( Vector3(-far_endpoint.x,-far_endpoint.y, far_endpoint.z ) );

	return true;
}

Vector<Plane> CameraMatrix::get_projection_planes(const Transform& p_transform) const {

	/** Fast Plane Extraction from combined modelview/projection matrices.
	 * References:
	 * http://www.markmorley.com/opengl/frustumculling.html
	 * http://www2.ravensoft.com/users/ggribb/plane%20extraction.pdf
	 */

	Vector<Plane> planes;

	const real_t * matrix = (const real_t*)this->matrix;

	Plane new_plane;

	///////--- Near Plane ---///////
	new_plane=Plane(matrix[ 3] + matrix[ 2],
		      matrix[ 7] + matrix[ 6],
		      matrix[11] + matrix[10],
		      matrix[15] + matrix[14]);

	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	planes.push_back( p_transform.xform(new_plane) );

	///////--- Far Plane ---///////
	new_plane=Plane(matrix[ 3] - matrix[ 2],
		      matrix[ 7] - matrix[ 6],
		      matrix[11] - matrix[10],
		      matrix[15] - matrix[14]);

	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	planes.push_back( p_transform.xform(new_plane) );


	///////--- Left Plane ---///////
	new_plane=Plane(matrix[ 3] + matrix[ 0],
		      matrix[ 7] + matrix[ 4],
		      matrix[11] + matrix[ 8],
		      matrix[15] + matrix[12]);

	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	planes.push_back( p_transform.xform(new_plane) );


	///////--- Top Plane ---///////
	new_plane=Plane(matrix[ 3] - matrix[ 1],
		      matrix[ 7] - matrix[ 5],
		      matrix[11] - matrix[ 9],
		      matrix[15] - matrix[13]);


	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	planes.push_back( p_transform.xform(new_plane) );


	///////--- Right Plane ---///////
	new_plane=Plane(matrix[ 3] - matrix[ 0],
		      matrix[ 7] - matrix[ 4],
		      matrix[11] - matrix[ 8],
		      matrix[15] - matrix[12]);


	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	planes.push_back( p_transform.xform(new_plane) );


	///////--- Bottom Plane ---///////
	new_plane=Plane(matrix[ 3] + matrix[ 1],
		      matrix[ 7] + matrix[ 5],
		      matrix[11] + matrix[ 9],
		      matrix[15] + matrix[13]);


	new_plane.normal=-new_plane.normal;
	new_plane.normalize();

	planes.push_back( p_transform.xform(new_plane) );

	return planes;
}



CameraMatrix CameraMatrix::inverse() const {

	CameraMatrix cm = *this;
	cm.invert();
	return cm;
}

void CameraMatrix::invert() {

	int i,j,k;
	int pvt_i[4], pvt_j[4];            /* Locations of pivot matrix */
	real_t pvt_val;                     /* Value of current pivot element */
	real_t hold;                        /* Temporary storage */
	real_t determinat;                  /* Determinant */

	determinat = 1.0;
	for (k=0; k<4; k++)  {
		/** Locate k'th pivot element **/
		pvt_val=matrix[k][k];            /** Initialize for search **/
		pvt_i[k]=k;
		pvt_j[k]=k;
		for (i=k; i<4; i++) {
			for (j=k; j<4; j++) {
				if (Math::absd(matrix[i][j]) > Math::absd(pvt_val)) {
					pvt_i[k]=i;
					pvt_j[k]=j;
					pvt_val=matrix[i][j];
				}
			}
		}

		/** Product of pivots, gives determinant when finished **/
		determinat*=pvt_val;
		if (Math::absd(determinat)<1e-7) {
			return; //(false);  /** Matrix is singular (zero determinant). **/
		}

		/** "Interchange" rows (with sign change stuff) **/
		i=pvt_i[k];
		if (i!=k) {               /** If rows are different **/
			for (j=0; j<4; j++) {
				hold=-matrix[k][j];
				matrix[k][j]=matrix[i][j];
				matrix[i][j]=hold;
			}
		}

		/** "Interchange" columns **/
		j=pvt_j[k];
		if (j!=k) {              /** If columns are different **/
			for (i=0; i<4; i++) {
				hold=-matrix[i][k];
				matrix[i][k]=matrix[i][j];
				matrix[i][j]=hold;
			}
		}

		/** Divide column by minus pivot value **/
		for (i=0; i<4; i++) {
			if (i!=k) matrix[i][k]/=( -pvt_val) ;
		}

		/** Reduce the matrix **/
		for (i=0; i<4; i++) {
			hold = matrix[i][k];
			for (j=0; j<4; j++) {
				if (i!=k && j!=k) matrix[i][j]+=hold*matrix[k][j];
			}
		}

		/** Divide row by pivot **/
		for (j=0; j<4; j++) {
			if (j!=k) matrix[k][j]/=pvt_val;
		}

		/** Replace pivot by reciprocal (at last we can touch it). **/
		matrix[k][k] = 1.0/pvt_val;
	}

	/* That was most of the work, one final pass of row/column interchange */
	/* to finish */
	for (k=4-2; k>=0; k--) { /* Don't need to work with 1 by 1 corner*/
		i=pvt_j[k];            /* Rows to swap correspond to pivot COLUMN */
		if (i!=k) {            /* If rows are different */
			for(j=0; j<4; j++) {
				hold = matrix[k][j];
				matrix[k][j]=-matrix[i][j];
				matrix[i][j]=hold;
			}
		}

		j=pvt_i[k];           /* Columns to swap correspond to pivot ROW */
		if (j!=k)             /* If columns are different */
			for (i=0; i<4; i++) {
			hold=matrix[i][k];
			matrix[i][k]=-matrix[i][j];
			matrix[i][j]=hold;
			}
	}


}

CameraMatrix::CameraMatrix() {

	set_identity();
}

CameraMatrix CameraMatrix::operator*(const CameraMatrix& p_matrix) const {

	CameraMatrix new_matrix;

	for( int j = 0; j < 4; j++ ) {
		for( int i = 0; i < 4; i++ ) {
			real_t ab = 0;
			for( int k = 0; k < 4; k++ )
				ab += matrix[k][i] * p_matrix.matrix[j][k] ;
			new_matrix.matrix[j][i] = ab;
		}
	}

	return new_matrix;
}

void CameraMatrix::set_light_bias() {

	real_t *m=&matrix[0][0];

	m[0]=0.5,
	m[1]=0.0,
	m[2]=0.0,
	m[3]=0.0,
	m[4]=0.0,
	m[5]=0.5,
	m[6]=0.0,
	m[7]=0.0,
	m[8]=0.0,
	m[9]=0.0,
	m[10]=0.5,
	m[11]=0.0,
	m[12]=0.5,
	m[13]=0.5,
	m[14]=0.5,
	m[15]=1.0;

}

void CameraMatrix::set_light_atlas_rect(const Rect2& p_rect) {

	real_t *m=&matrix[0][0];

	m[0]=p_rect.size.width,
	m[1]=0.0,
	m[2]=0.0,
	m[3]=0.0,
	m[4]=0.0,
	m[5]=p_rect.size.height,
	m[6]=0.0,
	m[7]=0.0,
	m[8]=0.0,
	m[9]=0.0,
	m[10]=1.0,
	m[11]=0.0,
	m[12]=p_rect.pos.x,
	m[13]=p_rect.pos.y,
	m[14]=0.0,
	m[15]=1.0;
}

CameraMatrix::operator String() const {

	String str;
	for (int i=0;i<4;i++)
		for (int j=0;j<4;j++)
			str+=String((j>0)?", ":"\n")+rtos(matrix[i][j]);

	return str;
}

real_t CameraMatrix::get_aspect() const {

	real_t w,h;
	get_viewport_size(w,h);
	return w/h;
}

int CameraMatrix::get_pixels_per_meter(int p_for_pixel_width) const {


	Vector3 result = xform(Vector3(1,0,-1));

	return int((result.x * 0.5 + 0.5) * p_for_pixel_width);

}

real_t CameraMatrix::get_fov() const {
	const real_t * matrix = (const real_t*)this->matrix;

	Plane right_plane=Plane(matrix[ 3] - matrix[ 0],
			matrix[ 7] - matrix[ 4],
			matrix[11] - matrix[ 8],
			- matrix[15] + matrix[12]);
	right_plane.normalize();

	return Math::rad2deg(Math::acos(Math::abs(right_plane.normal.x)))*2.0;
}


void CameraMatrix::make_scale(const Vector3 &p_scale) {

	set_identity();
	matrix[0][0]=p_scale.x;
	matrix[1][1]=p_scale.y;
	matrix[2][2]=p_scale.z;

}

void CameraMatrix::scale_translate_to_fit(const Rect3& p_aabb) {

	Vector3 min = p_aabb.pos;
	Vector3 max = p_aabb.pos+p_aabb.size;


	matrix[0][0]=2/(max.x-min.x);
	matrix[1][0]=0;
	matrix[2][0]=0;
	matrix[3][0]=-(max.x+min.x)/(max.x-min.x);

	matrix[0][1]=0;
	matrix[1][1]=2/(max.y-min.y);
	matrix[2][1]=0;
	matrix[3][1]=-(max.y+min.y)/(max.y-min.y);

	matrix[0][2]=0;
	matrix[1][2]=0;
	matrix[2][2]=2/(max.z-min.z);
	matrix[3][2]=-(max.z+min.z)/(max.z-min.z);

	matrix[0][3]=0;
	matrix[1][3]=0;
	matrix[2][3]=0;
	matrix[3][3]=1;
}

CameraMatrix::operator Transform() const {

	Transform tr;
	const real_t *m=&matrix[0][0];

	tr.basis.elements[0][0]=m[0];
	tr.basis.elements[1][0]=m[1];
	tr.basis.elements[2][0]=m[2];

	tr.basis.elements[0][1]=m[4];
	tr.basis.elements[1][1]=m[5];
	tr.basis.elements[2][1]=m[6];

	tr.basis.elements[0][2]=m[8];
	tr.basis.elements[1][2]=m[9];
	tr.basis.elements[2][2]=m[10];

	tr.origin.x=m[12];
	tr.origin.y=m[13];
	tr.origin.z=m[14];

	return tr;
}

CameraMatrix::CameraMatrix(const Transform& p_transform) {

	const Transform &tr = p_transform;
	real_t *m=&matrix[0][0];

	m[0]=tr.basis.elements[0][0];
	m[1]=tr.basis.elements[1][0];
	m[2]=tr.basis.elements[2][0];
	m[3]=0.0;
	m[4]=tr.basis.elements[0][1];
	m[5]=tr.basis.elements[1][1];
	m[6]=tr.basis.elements[2][1];
	m[7]=0.0;
	m[8]=tr.basis.elements[0][2];
	m[9]=tr.basis.elements[1][2];
	m[10]=tr.basis.elements[2][2];
	m[11]=0.0;
  	m[12]=tr.origin.x;
	m[13]=tr.origin.y;
	m[14]=tr.origin.z;
	m[15]=1.0;
}

CameraMatrix::~CameraMatrix()
{
}