/**

  * $Id: rendbkg.c,v 1.3 2006-09-12 12:16:36 nkeynes Exp $

  *

  * PVR2 background renderer. 

  *

  * Yes, it uses the same basic data structure. Yes, it needs to be handled

  * completely differently.

  *

  * Note: this would be really simple if GL did unclamped colour interpolation

  * but it doesn't (portably), which makes this roughly 2 orders of magnitude

  * more complicated than it otherwise would be.

  *

  * Copyright (c) 2005 Nathan Keynes.

  *

  * 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 2 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.

  */

 #include <sys/time.h>

 #include "pvr2/pvr2.h"

 #include <GL/glext.h>

 #include <math.h>

 #define MAX_CLAMP_LINES 8

 #define MAX_VERTEXES 256

 #define MAX_REGIONS  256

 /**

  * Structure to hold an unpacked vertex

  */

 struct vertex_all {

     float x,y,z;

     float u,v;

     float rgba[4];      /* Note - RGBA order, as preferred by GL */

     float spec_rgba[4];

 };

 #define FARGB_A(x) (((float)(((x)>>24)+1))/256.0)

 #define FARGB_R(x) (((float)((((x)>>16)&0xFF)+1))/256.0)

 #define FARGB_G(x) (((float)((((x)>>8)&0xFF)+1))/256.0)

 #define FARGB_B(x) (((float)(((x)&0xFF)+1))/256.0)

 /**

  * Compute the line where k = target_k, (where k is normally one of

  * r,g,b,a, or z) and determines the points at which the line intersects

  * the viewport (0,0,width,height).

  *

  * @param center_x the x value for the center position

  * @param center_y the y value for the center position

  * @param center_k the k value for the center position

  * @param width Width of the viewport (ie 640)

  * @param height Height of the viewport (ie 480)

  * @param target_k determine the line where k = this value, ie 1.0

  * @param detxy

  * @param target Array to write the resultant x,y pairs to (note this

  * function only sets x and y values).

  * @return number of vertexes written to the target.

  */

 static int compute_colour_line( float center_x, float center_y, float center_k, 

 		  int width, int height, float target_k,

 		  float detxy, float detxk, float detyk,

 		  struct vertex_all *target ) {

     int num_points = 0;

     float tmpk = (target_k - center_k) * detxy;

     float x0 = -1;

     float x1 = -1;

     if( detyk != 0 ) {

 	x0 = (tmpk - ((0-center_y)*detxk))/detyk + center_x; /* x where y=0 */

 	if( x0 >= 0.0 && x0 <= width ) {

 	    target[num_points].x = x0;

 	    target[num_points].y = 0.0;

 	    num_points++;

 	}

 	x1 = (tmpk - ((height-center_y)*detxk))/detyk + center_x; /* x where y=height */

 	if( x1 >= 0.0 && x1 <= width ) {

 	    target[num_points].x = x1;

 	    target[num_points].y = height;

 	    num_points++;

 	}

     }

     if( detxk != 0 ) {

 	if( x0 != 0.0 && x1 != 0.0 ) { /* If x0 == 0 or x1 == 0, then we already have this one */

 	    float y0 = (tmpk - ((0-center_x)*detyk))/detxk + center_y; /* y where x=0 */

 	    if( y0 >= 0.0 && y0 <= height ) {

 		target[num_points].x = 0.0;

 		target[num_points].y = y0;

 		num_points++;

 	    }

 	}

 	if( x0 != width && x1 != width ) {

 	    float y1 = (tmpk - ((width-center_x)*detyk))/detxk + center_y; /* y where x=width */

 	    if( y1 >= 0.0 && y1 <= height ) {

 		target[num_points].x = width;

 		target[num_points].y = y1;

 		num_points++;

 	    }

 	}

     }

     if( num_points == 0 || num_points == 2 ) {

 	/* 0 = no points - line doesn't pass through the viewport */

 	/* 2 = normal case - got 2 endpoints */

 	return num_points;

     } else {

 	ERROR( "compute_colour_line got bad number of points: %d", num_points );

 	return 0;

     }

 }

 /**

  * A region describes a portion of the screen, possibly subdivided by a line.

  * if region_left and region_right are -1, this is a terminal region that can

  * be rendered directly. Otherwise region_left and region_right refer two 

  * sub-regions that are separated by the line segment vertex1-vertex2.

  */

 struct bkg_region {

     /* Vertexes marking the line segment that splits this region */

     int vertex1;

     int vertex2;

     /* Index of the left sub-region */

     int region_left;

     /* Index of the right sub-region */

     int region_right;

 };

 /**

  * Convenience structure to bundle together the vertex and region data.

  */

 struct bkg_scene {

     int num_vertexes;

     int num_regions;

     struct vertex_all vertexes[MAX_VERTEXES];

     struct bkg_region regions[MAX_REGIONS];

 };

 void parse_vertexes( uint32_t *polygon, int num_vertexes, struct vertex_all *result )

 {

     uint32_t *vertexes = polygon + 3; 

     int i,m = 0;

     for( i=0; i<num_vertexes; i++ ) {

 	float *vertexf = (float *)vertexes;

 	result[i].x = vertexf[0];

 	result[i].y = vertexf[1];

 	result[i].z = vertexf[2];

 	uint32_t argb;

 	if( POLY1_TEXTURED(*polygon) ) {

 	    if( POLY1_UV16(*polygon) ) {

 		result[i].u = halftofloat(vertexes[m+3]>>16);

 		result[i].v = halftofloat(vertexes[m+3]);

 		argb = vertexes[m+4];

 		vertexes += 5;

 	    } else {

 		result[i].u = vertexf[m+3];

 		result[i].v = vertexf[m+4];

 		argb = vertexes[m+5];

 		vertexes += 6;

 	    }

 	} else {

 	    argb = vertexes[m+3];

 	    vertexes += 4;

 	}

 	result[i].rgba[0] = FARGB_R(argb);

 	result[i].rgba[1] = FARGB_G(argb);

         result[i].rgba[2] = FARGB_B(argb);

 	result[i].rgba[3] = FARGB_A(argb);

     }

 }

 /**

  * Constants returned by compute_line_intersection. Note that for these purposes,

  * "Left" means the point(s) result in a negative value in the line equation, while

  * "Right" means the points(s) result in a positive value in the line equation. The

  * exact meaning isn't particularly important though, as long as we're consistent

  * throughout this process

  */

 #define LINE_COLLINEAR 0   /* The line segments are part of the same line */

 #define LINE_SIDE_LEFT 1   /* The second line is entirely to the "left" of the first line */

 #define LINE_SIDE_RIGHT 2  /* The second line is entirely to the "right" of the first line */

 #define LINE_INTERSECT_FROM_LEFT 3 /* The lines intersect, and (x3,y3) is to the "left" of the first line */

 #define LINE_INTERSECT_FROM_RIGHT 4 /* The lines intersect, and (x3,y3) is to the "right" of the first line */

 #define LINE_SKEW 5        /* The line segments neither intersect nor do any of the above apply (should never happen here) */

 /**

  * Compute the intersection of two line segments, where 

  * (x1,y1)-(x2,y2) defines the target segment, and

  * (x3,y3)-(x4,y4) defines the line intersecting it.

  *

  * Based off work by Mukesh Prasad (http://www.acm.org/pubs/tog/GraphicsGems/index.html)

  *

  * @return one of the above LINE_* constants

  */

 static int compute_line_intersection( float x1, float y1,   /* First line segment */

 				      float x2, float y2,

 				      float x3, float y3,   /* Second line segment */

 				      float x4, float y4,

 				      float *x, float *y  )  /* Output value: */

 {

     float a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */

     float r1, r2, r3, r4;         /* test values */

     float denom;     /* Intermediate values */

     /* Compute a1, b1, c1, where line joining points 1 and 2

      * is "a1 x  +  b1 y  +  c1  =  0".

      */

     a1 = y2 - y1;

     b1 = x1 - x2;

     c1 = x2 * y1 - x1 * y2;

     /* Compute r3 and r4. */

     r3 = a1 * x3 + b1 * y3 + c1;

     r4 = a1 * x4 + b1 * y4 + c1;

     /* Check signs of r3 and r4.  If both point 3 and point 4 lie on

      * same side of line 1, the line segments do not intersect.

      */

     if( r3 == 0 && r4 == 0 ) {

 	return LINE_COLLINEAR;

     } else if( r3 <= 0 && r4 <= 0 ) {

 	return LINE_SIDE_LEFT;

     } else if( r3 >= 0 && r4 >= 0 ) {

 	return LINE_SIDE_RIGHT;

     }

     /* Compute a2, b2, c2 */

     a2 = y4 - y3;

     b2 = x3 - x4;

     c2 = x4 * y3 - x3 * y4;

     /* Compute r1 and r2 */

     r1 = a2 * x1 + b2 * y1 + c2;

     r2 = a2 * x2 + b2 * y2 + c2;

     /* Check signs of r1 and r2.  If both point 1 and point 2 lie

      * on same side of second line segment, the line segments do

      * not intersect.

      */

     if ( r1 != 0 && r2 != 0 &&

          signbit(r1) == signbit(r2) ) {

         return LINE_SKEW; /* Should never happen */

     }

     /* Cmpute intersection point. 

      */

     denom = a1 * b2 - a2 * b1;

     if ( denom == 0 )

         return LINE_COLLINEAR; /* Should never get to this point either */

     *x = (b1 * c2 - b2 * c1) / denom;

     *y = (a2 * c1 - a1 * c2) / denom;

     if( r3 <= 0 && r4 >= 0 ) {

 	return LINE_INTERSECT_FROM_LEFT;

     } else {

 	return LINE_INTERSECT_FROM_RIGHT;

     }

 }

 /**

  * Given a set of vertexes and a line segment to use to split them, generates

  * two sets of vertexes representing the polygon on either side of the line

  * segment. This method preserves the winding direction of the input vertexes.

  */

 static void compute_subregions( struct bkg_scene *scene,

 				int splitv1, int splitv2,

 				int *vertex_in, int num_vertex_in,

 				int *left_vertex_out, int *num_left_vertex_out,

 				int *right_vertex_out, int *num_right_vertex_out )

 {

     float x1 = scene->vertexes[splitv1].x;

     float y1 = scene->vertexes[splitv1].y;

     float x2 = scene->vertexes[splitv2].x;

     float y2 = scene->vertexes[splitv2].y;

     float a1 = y2 - y1;

     float b1 = x1 - x2;

     float c1 = x2 * y1 - x1 * y2;

     int i;

     *num_left_vertex_out = 0;

     *num_right_vertex_out = 0;

     int last = 0;

     for( i=0; i<num_vertex_in; i++ ) {

 	struct vertex_all *vertex = &scene->vertexes[vertex_in[i]];

 	float r = a1 * vertex->x + b1 * vertex->y + c1;

 	if( r <= 0 ) {

 	    if( last == 1 ) {

 		/* cross-point. add the split vertexes */

 		int v1 = vertex_in[i-1];

 		int v2 = vertex_in[i];

 		/* Determine which point is closer to the line. Strictly speaking

 		 * one of them must be ON the line, but this way allows for floating

 		 * point inaccuracies.

 		 */

 		float a2 = scene->vertexes[v2].y - scene->vertexes[v1].y;

 		float b2 = scene->vertexes[v1].x - scene->vertexes[v2].x;

 		float c2 = scene->vertexes[v2].x * scene->vertexes[v1].y - 

 		    scene->vertexes[v1].x * scene->vertexes[v2].y;

 		float r1 = a2 * x1 + b2 * y1 + c2;

 		float r2 = a2 * x2 + b2 * y2 + c2;

 		if( fabsf(r1) > fabs(r2) ) {

 		    int tmp = splitv1;

 		    splitv1 = splitv2;

 		    splitv2 = tmp;

 		}

 		right_vertex_out[(*num_right_vertex_out)++] = splitv1;

 		right_vertex_out[(*num_right_vertex_out)++] = splitv2;

 		left_vertex_out[(*num_left_vertex_out)++] = splitv2;

 		left_vertex_out[(*num_left_vertex_out)++] = splitv1;

 		last = 2;

 	    } else if( last != 2 ) {

 		last = -1;

 	    }

 	    left_vertex_out[(*num_left_vertex_out)++] = vertex_in[i];

 	} else {

 	    if( last == -1 ) {

 		/* cross-point. add the split vertexes */

 		int v1 = vertex_in[i-1];

 		int v2 = vertex_in[i];

 		/* Determine which point is closer to the line. Strictly speaking

 		 * one of them must be ON the line, but this way allows for floating

 		 * point inaccuracies.

 		 */

 		float a2 = scene->vertexes[v2].y - scene->vertexes[v1].y;

 		float b2 = scene->vertexes[v1].x - scene->vertexes[v2].x;

 		float c2 = scene->vertexes[v2].x * scene->vertexes[v1].y - 

 		    scene->vertexes[v1].x * scene->vertexes[v2].y;

 		float r1 = a2 * x1 + b2 * y1 + c2;

 		float r2 = a2 * x2 + b2 * y2 + c2;

 		if( fabsf(r1) > fabs(r2) ) {

 		    int tmp = splitv1;

 		    splitv1 = splitv2;

 		    splitv2 = tmp;

 		}

 		left_vertex_out[(*num_left_vertex_out)++] = splitv1;

 		left_vertex_out[(*num_left_vertex_out)++] = splitv2;

 		right_vertex_out[(*num_right_vertex_out)++] = splitv2;

 		right_vertex_out[(*num_right_vertex_out)++] = splitv1;

 		last = 2;

 	    } else if( last != 2 ) {

 		last = 1;

 	    }

 	    right_vertex_out[(*num_right_vertex_out)++] = vertex_in[i];

 	}

     }

 }

 /**

  * Subdivide the region tree by splitting it along a given line.

  * 

  * @param scene  current bkg scene data

  * @param region current region under examination

  * @param vertex1 first vertex of the new line segment

  * @param vertex2 second vertex of the new line segment

  */

 static void bkg_region_subdivide( struct bkg_scene *scene, int region, int vertex1, int vertex2 ) {

     struct bkg_region *this_region = &scene->regions[region];

     if( scene->regions[region].region_left == -1 || scene->regions[region].region_right == -1 ) {

 	/* Reached the end of the tree. Setup new left+right regions */

 	int i = scene->num_regions;

 	scene->regions[i].region_left = scene->regions[i].region_right = -1;

 	scene->regions[i+1].region_left = scene->regions[i+1].region_right = -1;

 	this_region->region_left = i;

 	this_region->region_right = i+1;

 	this_region->vertex1 = vertex1;

 	this_region->vertex2 = vertex2;

 	scene->num_regions += 2;

     } else {

 	float x,y;

 	int thisv1 = this_region->vertex1;

 	int thisv2 = this_region->vertex2;

 	int vertex3;

 	int status = 

 	    compute_line_intersection( scene->vertexes[thisv1].x, scene->vertexes[thisv1].y,

 				       scene->vertexes[thisv2].x, scene->vertexes[thisv2].y,

 				       scene->vertexes[vertex1].x, scene->vertexes[vertex1].y,

 				       scene->vertexes[vertex2].x, scene->vertexes[vertex2].y,

 				       &x, &y );

 	switch( status ) {

 	case LINE_INTERSECT_FROM_LEFT:

 	    /* if new line segment intersects our current line segment,

 	     * subdivide the segment (add a new vertex) and recurse on both

 	     * sub trees 

 	     */

 	    /* Compute split-point vertex */

 	    vertex3 = scene->num_vertexes++;

 	    scene->vertexes[vertex3].x = x;

 	    scene->vertexes[vertex3].y = y;

 	    /* Recurse */

 	    bkg_region_subdivide( scene, scene->regions[region].region_left, vertex1,vertex3 );

 	    bkg_region_subdivide( scene, scene->regions[region].region_right, vertex3, vertex2 );

 	    break;

 	case LINE_INTERSECT_FROM_RIGHT:

 	    /* Same except line runs in the opposite direction */

 	    vertex3 = scene->num_vertexes++;

 	    scene->vertexes[vertex3].x = x;

 	    scene->vertexes[vertex3].y = y;

 	    /* Recurse */

 	    bkg_region_subdivide( scene, scene->regions[region].region_left, vertex2,vertex3 );

 	    bkg_region_subdivide( scene, scene->regions[region].region_right, vertex3, vertex1 );

 	    break;

 	case LINE_COLLINEAR:

 	case LINE_SKEW:

 	    /* Collinear - ignore */

 	    break;

 	case LINE_SIDE_LEFT:

 	    /* else if line segment passes through the left sub-region alone,

 	     * left-recurse only.

 	     */

 	    bkg_region_subdivide( scene, scene->regions[region].region_left, vertex1, vertex2 );

 	    break;

 	case LINE_SIDE_RIGHT:

 	    /* Otherwise line segment passes through the right sub-region alone,

 	     * so right-recurse.

 	     */

 	    bkg_region_subdivide( scene, scene->regions[region].region_right, vertex1, vertex2 );

 	    break;

 	}

     }

 }

 /**

  * Compute the values for an array of vertexes, given x,y for each

  * vertex and the base 3-vertex triple used to define the background

  * plane. Essentially the base vertexes are used to find the

  * plane equation for each of z,a,r,g,b,etc, which is then solved for

  * each of the required compute vertexes (normally the corner points).

  *

  * @param base The 3 vertexes supplied as the background definition

  * @param compute An array of vertexes to compute. x and y must be

  *   preset, other values are computed.

  */

 static void bkg_compute_scene( struct vertex_all *base, int width, int height,

 				struct bkg_scene *scene )

 {

     struct vertex_all center;

     struct vertex_all diff0, diff1;

     int i,k;

     center.x = base[1].x;

     center.y = base[1].y;

     center.z = base[1].z;

     diff0.x = base[0].x - base[1].x;

     diff0.y = base[0].y - base[1].y;

     diff0.z = base[0].z - base[1].z;

     diff1.x = base[2].x - base[1].x;

     diff1.y = base[2].y - base[1].y;

     diff1.z = base[2].z - base[1].z;

     float detxy = ((diff1.y) * (diff0.x)) - ((diff0.y) * (diff1.x));

     /* Corner points first */

     scene->vertexes[0].x = 0.0;

     scene->vertexes[0].y = 0.0;

     scene->vertexes[1].x = width;

     scene->vertexes[1].y = 0.0;

     scene->vertexes[2].x = width;

     scene->vertexes[2].y = height;

     scene->vertexes[3].x = 0.0;

     scene->vertexes[3].y = height;

     scene->regions[0].region_left = -1;

     scene->regions[0].region_right = -1;

     scene->num_vertexes = 4;

     scene->num_regions = 1;

     if( detxy == 0 ) {

 	/* The points lie on a single line - no plane for you. Use the values

 	 * from the 3rd point for the whole screen.

 	 */

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

 	    scene->vertexes[i].rgba[0] = base[2].rgba[0];

 	    scene->vertexes[i].rgba[1] = base[2].rgba[1];

 	    scene->vertexes[i].rgba[2] = base[2].rgba[2];

 	    scene->vertexes[i].rgba[3] = base[2].rgba[3];

 	    scene->vertexes[i].u = base[2].u;

 	    scene->vertexes[i].v = base[2].v;

 	}

     } else {

 	/* Compute the colour values at each corner */

 	center.rgba[0] = base[1].rgba[0];

 	center.rgba[1] = base[1].rgba[1];

 	center.rgba[2] = base[1].rgba[2];

 	center.rgba[3] = base[1].rgba[3];

 	diff0.rgba[0] = base[0].rgba[0] - center.rgba[0];

 	diff0.rgba[1] = base[0].rgba[1] - center.rgba[1];

 	diff0.rgba[2] = base[0].rgba[2] - center.rgba[2];

 	diff0.rgba[3] = base[0].rgba[3] - center.rgba[3];

 	diff0.u = base[0].u - center.u;

 	diff0.v = base[0].v - center.v;

 	diff1.rgba[0] = base[2].rgba[0] - center.rgba[0];

 	diff1.rgba[1] = base[2].rgba[1] - center.rgba[1];

 	diff1.rgba[2] = base[2].rgba[2] - center.rgba[2];

 	diff1.rgba[3] = base[2].rgba[3] - center.rgba[3];

 	diff1.u = base[2].u - center.u;

 	diff1.v = base[2].v - center.v;

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

 	    float t = ((scene->vertexes[i].x - center.x) * diff1.y -

 		       (scene->vertexes[i].y - center.y) * diff1.x) / detxy;

 	    float s = ((scene->vertexes[i].y - center.y) * diff0.x -

 		       (scene->vertexes[i].x - center.x) * diff0.y) / detxy;

 	    scene->vertexes[i].z = center.z + (t*diff0.z) + (s*diff1.z);

 	    scene->vertexes[i].rgba[0] = center.rgba[0] + (t*diff0.rgba[0]) + (s*diff1.rgba[0]);

 	    scene->vertexes[i].rgba[1] = center.rgba[1] + (t*diff0.rgba[1]) + (s*diff1.rgba[1]);

 	    scene->vertexes[i].rgba[2] = center.rgba[2] + (t*diff0.rgba[2]) + (s*diff1.rgba[2]);

 	    scene->vertexes[i].rgba[3] = center.rgba[3] + (t*diff0.rgba[3]) + (s*diff1.rgba[3]);

 	    scene->vertexes[i].u = center.u + (t*diff0.u) + (s*diff1.u);

 	    scene->vertexes[i].v = center.v + (t*diff0.v) + (s*diff1.v);

 	}

 	/* Check for values > 1.0 | < 0.0 */

 	for( k=0; k<4; k++ ) {

 	    float detyk = ((diff1.y) * (diff0.rgba[k])) - ((diff0.y)*(diff1.rgba[k]));

 	    float detxk = ((diff0.x) * (diff1.rgba[k])) - ((diff1.x)*(diff0.rgba[k]));

 	    if( scene->vertexes[0].rgba[k] > 1.0 || scene->vertexes[1].rgba[k] > 1.0 || 

 		scene->vertexes[2].rgba[k] > 1.0 || scene->vertexes[3].rgba[k] > 1.0 ) {

 		int v1 = scene->num_vertexes;

 		scene->num_vertexes += compute_colour_line(center.x, center.y, center.rgba[k],

 						    width, height, 1.0,

 						    detxy, detxk, detyk, 

 						    scene->vertexes+scene->num_vertexes );

 		if( scene->num_vertexes != v1 ) {

 		    bkg_region_subdivide( scene, 0, v1, v1+1 );

 		}

 	    }

 	    if( scene->vertexes[0].rgba[k] < 0.0 || scene->vertexes[1].rgba[k] < 0.0 || 

 		scene->vertexes[2].rgba[k] < 0.0 || scene->vertexes[3].rgba[k] < 0.0 ) {

 		int v1 = scene->num_vertexes;

 		scene->num_vertexes += compute_colour_line(center.x, center.y, center.rgba[k],

 						    width, height, 0.0,

 						    detxy, detxk, detyk, 

 						    scene->vertexes+scene->num_vertexes );

 		if( scene->num_vertexes != v1 ) {

 		    bkg_region_subdivide( scene, 0, v1, v1+1 );

 		}

 	    }

 	}

 	/* Finally compute the colour values for all vertexes 

 	 * (excluding the 4 we did upfront) */

 	for( i=4; i<scene->num_vertexes; i++ ) {

 	    float t = ((scene->vertexes[i].x - center.x) * diff1.y -

 		       (scene->vertexes[i].y - center.y) * diff1.x) / detxy;

 	    float s = ((scene->vertexes[i].y - center.y) * diff0.x -

 		       (scene->vertexes[i].x - center.x) * diff0.y) / detxy;

 	    scene->vertexes[i].z = center.z + (t*diff0.z) + (s*diff1.z);

 	    scene->vertexes[i].rgba[0] = center.rgba[0] + (t*diff0.rgba[0]) + (s*diff1.rgba[0]);

 	    scene->vertexes[i].rgba[1] = center.rgba[1] + (t*diff0.rgba[1]) + (s*diff1.rgba[1]);

 	    scene->vertexes[i].rgba[2] = center.rgba[2] + (t*diff0.rgba[2]) + (s*diff1.rgba[2]);

 	    scene->vertexes[i].rgba[3] = center.rgba[3] + (t*diff0.rgba[3]) + (s*diff1.rgba[3]);

 	    scene->vertexes[i].u = center.u + (t*diff0.u) + (s*diff1.u);

 	    scene->vertexes[i].v = center.v + (t*diff0.v) + (s*diff1.v);

 	}

     }

 }

 /**

  * Render a bkg_region.

  * @param scene the background scene data

  * @param region the region to render

  * @param vertexes the vertexes surrounding the region

  * @param num_vertexes the number of vertexes in the vertex array

  */

 void bkg_render_region( struct bkg_scene *scene, int region, int *vertexes, int num_vertexes,

 			uint32_t poly1 )

 {

     if( scene->regions[region].region_left == -1 && scene->regions[region].region_right == -1 ) {

 	/* Leaf node - render the points as given */

 	int i,k;

 	glBegin(GL_POLYGON);

 	for( i=0; i<num_vertexes; i++ ) {

 	    k = vertexes[i];

 	    glColor4fv(scene->vertexes[k].rgba);

 	    if( POLY1_TEXTURED(poly1) ) {

 		glTexCoord2f(scene->vertexes[k].u, scene->vertexes[k].v);

 	    }

 	    glVertex3f(scene->vertexes[k].x, scene->vertexes[k].y, scene->vertexes[k].z);

 	}

 	glEnd();

     } else {

 	/* split the region into left and right regions */

 	int left_vertexes[num_vertexes+1];

 	int right_vertexes[num_vertexes+1];

 	int num_left = 0;

 	int num_right = 0;

 	struct bkg_region *reg = &scene->regions[region];

 	compute_subregions( scene, reg->vertex1, reg->vertex2, vertexes, num_vertexes,

 			    left_vertexes, &num_left, right_vertexes, &num_right );

 	bkg_render_region( scene, reg->region_left, left_vertexes, num_left, poly1 );

 	bkg_render_region( scene, reg->region_right, right_vertexes, num_right, poly1 );

     }

 }

 void render_backplane( uint32_t *polygon, uint32_t width, uint32_t height, uint32_t mode ) {

     struct vertex_all vertex[3];

     int screen_vertexes[4] = {0,1,2,3};

     struct bkg_scene scene;

     int i,j,k, num_vertexes;

     parse_vertexes(polygon, 3, vertex);

     render_set_context(polygon, 0);

     glDisable(GL_CULL_FACE);

     glDisable(GL_DEPTH_TEST);

     glBlendFunc(GL_ONE, GL_ZERO); /* For now, just disable alpha blending on the bkg */

     bkg_compute_scene(vertex, width, height, &scene);

     bkg_render_region(&scene, 0, screen_vertexes, 4, *polygon);

 }