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Code for image on Bezier triangular patch in images.
#version 3.7;
//
#include "colors.inc"
#include "metals.inc"
global_settings {max_trace_level 15 assumed_gamma 1.0}
camera {orthographic location <50,30,10> look_at <0,20,0>}
#declare llevel = 1.2;
light_source {<-3000,2000,-3000> rgb <llevel, llevel,llevel> shadowless }
background{White}
//*********************************************************************************************************************
*****
// TRIANGULAR BEZIER THIN PATCH
//*********************************************************************************************************************
*****
//
// Topologically, u is along the x axis, v is up the y axis. w = 1 - u - v
// We take v for the rows, u for the columns
//
// LoD Reduces the number of segments from that passed in. 0 a single
triangle. 4 uses segs as passed.
// polytype NOT USED. The triangular shape chooses the way we split a
quadrilateral into two triangles.
// debug_on = 0 nothing, = 1 puts spheres at knots, = 2 puts smaller spheres
at vertices, = 3 puts little cones in the direction of the normals.
// segs Number of segments on all sides.
// vertex_vects = array[10] contains the control knots as 3 vectors, going round
the edge, starting at a vertex, last is the single middle knot.
//
#macro SF_bezier_thin_tri_patch(LoD,polytype,debug_on,segs,vertex_vects)
//
#if(LoD = 0)
#local nsegs = 1;
#end
//
#if(LoD = 1)
#local nsegs = ceil(segs/10);
#end
//
#if(LoD = 2)
#local nsegs = ceil(segs/5);
#end
//
#if(LoD = 3)
#local nsegs = ceil(segs/2);
#end
//
#if(LoD > 3)
#local nsegs = segs;
#end
//
// Extract the control points into a readable format
//
#local p1 = vertex_vects[0];
#local p2 = vertex_vects[1];
#local p3 = vertex_vects[2];
#local p4 = vertex_vects[3];
#local p5 = vertex_vects[4];
#local p6 = vertex_vects[5];
#local p7 = vertex_vects[6];
#local p8 = vertex_vects[7];
#local p9 = vertex_vects[8];
#local p10 = vertex_vects[9];
//
#local onestrip = 0;
#if(nsegs = 1)
#local onestrip = 1;
#end
//
#if(onestrip = 1)
// Do a single triangle
#if(debug_on>0)
union{
#end
triangle{p1, p4, p7 }
#if(debug_on>0)
#local len_1 = vlength(p1-p4);
#local len_2 = vlength(p1-p7);
#local len_3 = vlength(p4-p7);
#local std_len = max(len_1,len_2,len_3)/100;
union{
sphere{p1 std_len }
sphere{p4 std_len }
sphere{p7 std_len }
pigment{Red}
}
}
#end
//
#else
// At least 2 by 2
union{
//
// De-bugging
#if(debug_on>0)
#local len_1 = vlength(p1-p4);
#local len_2 = vlength(p1-p7);
#local len_3 = vlength(p4-p7);
#local std_len = max(len_1,len_2,len_3)/100;
union{
sphere{p1 std_len pigment{Red}}
sphere{p2 std_len pigment{Orange}}
sphere{p3 std_len pigment{Yellow}}
sphere{p4 std_len pigment{Green}}
sphere{p5 std_len pigment{Cyan}}
sphere{p6 std_len pigment{Blue}}
sphere{p7 std_len pigment{Magenta}}
sphere{p8 std_len pigment{Black}}
sphere{p9 std_len pigment{Blue}}
sphere{p10 std_len pigment{Red}}
}
#end
//
// Generate the low points for the lowest strip
//
#local row_low_points = array[nsegs + 1];
#local row_low_normals = array[nsegs + 1];
#local row_high_points = array[nsegs + 1];
#local row_high_normals = array[nsegs + 1];
//
#local jcount = 0;
#while(jcount < nsegs+1)
#local uco = jcount/nsegs;
#local fu1 = pow(1-uco,3);
#local du1 = -3*pow(1-uco,2);
#local fu2 = 3*pow(1-uco,2)*uco;
#local du2 = 3*pow(1-uco,2) - 6*(1-uco)*uco;
#local fu3 = 3*(1-uco)*uco*uco;
#local du3 = -3*uco*uco + 6*(1-uco)*uco;
#local fu4 = pow(uco,3);
#local du4 = 3*pow(uco,2);
// Points
#local upoint = p1*fu1 + p2*fu2 + p3*fu3 + p4*fu4;
#local row_low_points[jcount] = upoint;
// Normals
#local tangudir = p1*du1 + p2*du2 + p3*du3 + p4*du4;
#local tangvdir = (p9-p1)*3*pow(1-uco,2) +
(p10-p2)*6*(1-uco)*uco + (p5-p3)*uco*uco;
#local row_low_normals[jcount] = vnormalize(vcross(tangvdir,tangudir));
//
#local jcount = jcount + 1;
#end
//
// Main loops over the strips (v changes) and along the strips (u changes)
//
#local icount = 0;
#while(icount < nsegs)
#local vco = (icount+1)/nsegs;
//
#local fv1 = pow(1-vco,3);
#local dv1 = -3*pow(1-vco,2);
#local fv2 = 3*pow(1-vco,2)*vco;
#local dv2 = 3*pow(1-vco,2) - 6*(1-vco)*vco;
#local fv3 = 3*(1-vco)*vco*vco;
#local dv3 = -3*vco*vco + 6*(1-vco)*vco;
#local fv4 = pow(vco,3);
#local dv4 = 3*pow(vco,2);
//
#local row_high_points[0] = p1*fv1 + p9*fv2 + p8*fv3 + p7*fv4;
//
#local tangvdir = p1*dv1 + p9*dv2 + p8*dv3 + p7*dv4;;
#local tangudir = (p2-p1)*3*(1-vco)*(1-vco) +
(p10-p9)*6*vco*(1-vco) + (p6-p8)*3*vco*vco;
#local row_high_normals[0] = vnormalize(vcross(tangvdir,tangudir));
//
#local jcount = 0;
#while(jcount < nsegs - icount - 1)
#local uco = (jcount+1)/nsegs;
#local wco = 1 - uco - vco;
#local f1 = pow(wco,3);
#local du1 = -3*pow(wco,2);
#local dv1 = du1;
#local f2 = 3*wco*wco*uco;
#local du2 = 3*wco*wco - 6*wco*uco;
#local dv2 = -6*wco*uco;
#local f3 = 3*wco*uco*uco;
#local du3 = -3*uco*uco + 6*wco*uco;
#local dv3 = -3*uco*uco;
#local f4 = pow(uco,3);
#local du4 = 3*pow(uco,2);
#local dv4 = 0;
#local f5 = 3*uco*uco*vco;
#local du5 = 6*uco*vco;
#local dv5 = 3*uco*uco;
#local f6 = 3*uco*vco*vco;
#local du6 = 3*vco*vco;
#local dv6 = 6*uco*vco;
#local f7 = pow(vco,3);
#local du7 = 0;
#local dv7 = 3*vco*vco;
#local f8 = 3*wco*vco*vco;
#local du8 = -3*vco*vco;
#local dv8 = -3*vco*vco + 6*wco*vco;
#local f9 = 3*wco*wco*vco;
#local du9 = -6*wco*vco;
#local dv9 = 3*wco*wco -6*wco*vco;
#local f10 = 6*uco*vco*wco;
#local du10 = 6*vco*wco - 6*uco*vco;
#local dv10 = 6*uco*wco - 6*uco*vco;
//
#local row_high_points[jcount+1] = p1*f1 + p2*f2 + p3*f3 + p4*f4 +
p5*f5 + p6*f6 + p7*f7 + p8*f8 + p9*f9 + p10*f10;
#local tangudir = p1*du1 + p2*du2 + p3*du3 + p4*du4 +
p5*du5 + p6*du6 + p7*du7 + p8*du8 + p9*du9 + p10*du10;
#local tangvdir = p1*dv1 + p2*dv2 + p3*dv3 + p4*dv4 +
p5*dv5 + p6*dv6 + p7*dv7 + p8*dv8 + p9*dv9 + p10*dv10;
#local row_high_normals[jcount+1] = vnormalize(vcross(tangvdir,tangudir));
//
#local pq1 = row_low_points[ jcount];
#local nq1 = row_low_normals[ jcount];
#local pq2 = row_low_points[ jcount+1];
#local nq2 = row_low_normals[ jcount+1];
#local pq3 = row_high_points[ jcount+1];
#local nq3 = row_high_normals[jcount+1];
#local pq4 = row_high_points[ jcount];
#local nq4 = row_high_normals[jcount];
//
smooth_triangle{pq1,nq1,pq2,nq2,pq4,nq4}
smooth_triangle{pq2,nq2,pq3,nq3,pq4,nq4}
//
// Put in some debug vertices
#if(debug_on > 1)
sphere{pq1 std_len/2 pigment{Blue}}
sphere{pq2 std_len/2 pigment{Blue}}
sphere{pq3 std_len/2 pigment{Blue}}
sphere{pq4 std_len/2 pigment{Blue}}
#end
// Put in some debug normals
#if(debug_on > 2)
cone{pq1 std_len/2 pq1+5*std_len*nq1 0 pigment{Blue}}
cone{pq2 std_len/2 pq2+5*std_len*nq2 0 pigment{Blue}}
cone{pq3 std_len/2 pq3+5*std_len*nq3 0 pigment{Blue}}
cone{pq4 std_len/2 pq4+5*std_len*nq4 0 pigment{Blue}}
#end
//
// Last triangle
//
#local jcount = jcount + 1;
#end
// Last triangle in row
#local pq5 = row_low_points[ jcount+1];
#local nq5 = row_low_normals[jcount+1];
//
smooth_triangle{pq2,nq2,pq5,nq5,pq3,nq3}
//
#if(debug_on = 2)
sphere{pq5 std_len/2 pigment{Blue}}
#end
#if(debug_on > 2)
cone{pq5 std_len/2 pq5+5*std_len*nq5 0 pigment{Blue}}
#end
//
#local row_low_points = row_high_points;
#local row_low_normals = row_high_normals;
//
#local icount = icount + 1;
#end
// Single triangle in top row. row_low_points[0] seems to point to p7 for a
reason I haven't worked out.
#local vco = (nsegs-1)/nsegs;
#local fv1 = pow(1-vco,3);
#local dv1 = -3*pow(1-vco,2);
#local fv2 = 3*pow(1-vco,2)*vco;
#local dv2 = 3*pow(1-vco,2) - 6*(1-vco)*vco;
#local fv3 = 3*(1-vco)*vco*vco;
#local dv3 = -3*vco*vco + 6*(1-vco)*vco;
#local fv4 = pow(vco,3);
#local dv4 = 3*pow(vco,2);
#local pq1 = p1*fv1 + p9*fv2 + p8*fv3 + p7*fv4;
#local tangvdir = p1*dv1 + p9*dv2 + p8*dv3 + p7*dv4;
#local tangudir = (p2-p1)*3*(1-vco)*(1-vco) + (p10-p9)*6*vco*(1-vco) +
(p6-p8)*3*vco*vco;
#local nq1 = vnormalize(vcross(tangvdir,tangudir));
#local pq2 = row_low_points[ 1];
#local nq2 = row_low_normals[1];
#local n7 = vnormalize(vcross(p6-p7,p8-p7));
// sphere{pq1 0.5 pigment{Yellow}}
// sphere{pq2 0.5 pigment{Yellow}}
//
smooth_triangle{pq1,nq1,pq2,nq2,p7,n7}
//
#if(debug_on = 2)
sphere{p7 std_len/2 pigment{Blue}}
#end
#if(debug_on > 2)
cone{p7 std_len/2 p7+5*std_len*n7 0 pigment{Blue}}
#end
//
} // End of the main union
#end
//
#end
//*********************************************************************************************************************
*************************
#declare LoD = 4;
#declare polytype = 1;
#declare debug_on = 3;
#declare segs = 25;
//
#declare vertex_vects = array[10]{<-60, 0, 0>,
<-40,15,-30>,
<-20,15,-30>,
< 0, 0,-30>,
< 0,40,-10>,
< 0,40, 10>,
< 0, 0, 30>,
<-20,15, 30>,
<-40,15, 30>,
<-30,60, 0>};
//
object{SF_bezier_thin_tri_patch(LoD,polytype,debug_on,segs,vertex_vects)
texture{T_Chrome_3C}}
box{<-70,-1,-40> <10,0,40> pigment{Green}}
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