Parametric shapes
built-in object
Warning:
Mike Williams wrote in his great
"Isosurface Tutorial" :
"Parametric surfaces render very slowly in POV-Ray ..." and unfortunately he is right!
Parametric equations are an alternative way of defining equations for 3d surfaces.
Syntax sample:
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// --- parametric surface ---
parametric{
function{ u } //x(u,v) or x
function{ u*v } //y(u,v) or f(x,z)
function{ v } //z(u,v) or z
<-1,-1>,<1,1> // start, end (u,v)
contained_by{box{<-1,-1,-1>,<1,1,1>}}
max_gradient 5
accuracy 0.0035
precompute 18 x,y,z
texture{
pigment{ color rgb<1,1,1> *1.2}
finish { phong 0.5 }
}
scale 0.5
rotate <0, 0, 0>
translate < 0, 0.5, 0>
} // end of parametric ------ |
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parametric{
function{ sin(u) } // x(u,v) or x
function{ cos(u) } // y(u,v) or f(x,z)
function{ v } // z(u,v) or z
<0,-2>,<2*pi,2> // start, end(u,v)
contained_by {box {<-2,-2,-2>,<2,2,2>}}
max_gradient 7
accuracy 0.005
precompute 18 x,y,z
texture{
pigment{ color rgb<1,1,1>}
finish { phong 0.5 }}
scale 0.5
} // end of parametric ------ |
 |
parametric{
function{ sin(u)+0.25*sin(v*2*pi)} // x(u,v)
function{ cos(u) } // y(u,v)
function{ v } // z(u,v)
<0,-2>,<2*pi,2> // start, end(u,v)
contained_by {box {<-2,-2,-2>,<2,2,2>}}
max_gradient 7
accuracy 0.005
precompute 18 x,y,z
texture{
pigment{ color rgb<1,1,1>*.8}
finish { phong 0.1 }}
scale 0.5
} // end of parametric ------ |
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parametric{
function{ u } //x(u,v)
function{ 0.25*sin(u*2*pi)} //y(u,v) or f(x,z)
function{ v } //z(u,v)
<-4,-2>,<4,2> // start, end of (u,v)
contained_by {box {<-1,-1,-1>,<1,1,1>}}
max_gradient 2
accuracy 0.0035
precompute 18 x,y,z
texture {
pigment{ color rgb<1,1,1>*1.2}
finish { phong 0.5 } }
scale 0.5
} // end of parametric ------ |
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parametric{
function{ u } //x(u,v)
function{ 0.5*v*sin(u*2*pi)}//y(u,v)
function{ v } //z(u,v)
<-4,-2>,<4,2> // start, end (u,v)
contained_by {box {<-1,-1,-1>,<1,1,1>}}
max_gradient 5
accuracy 0.0035
precompute 18 x,y,z
texture {
pigment{ color rgb<1,1,1>*1.2}
finish { phong 0.5 } }
scale 0.5
} // end of parametric ----- |
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parametric{
function{ u } //x(u,v)
function{ 0.15*sin(u*4*pi) } //y(u,v)
function{ v } //z(u,v)
<-4,-2>,<4,2> // start, end of (u,v)
contained_by {box {<-1,-1,-1>,<1,1,1>}}
max_gradient 3
accuracy 0.0035
precompute 18 x,y,z
texture {
pigment{ color rgb<1,1,1>*1.2}
finish { phong 0.5 } }
scale 0.5
} // end of parametric ----- |
 |
parametric{
function{ u } //x(u,v) or x
function{ 0.05*(sin(v*4*pi)+sin(u*4*pi))}
function{ v } //z(u,v) or z
<-4,-2>,<4,2> // start, end of (u,v)
contained_by {box {<-1,-1,-1>,<1,1,1>}}
max_gradient 2
accuracy 0.0035
precompute 18 x,y,z
texture {
pigment{ color rgb<1,1,1>}
finish { phong 0.5 } }
scale 0.5
} // end of parametric ----- |
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Conical screw:
parametric{
function{ u*v*sin(15*v) } //x(u,v)
function{ v } //y(u,v)
function{ u*v*cos(15*v) } //z(u,v)
<0,-1>,<1,1> // start, end (u,v)
contained_by {box {<-1,-1,-1>,<1,1,1>}}
max_gradient 5
accuracy 0.0035
precompute 18 x,y,z
texture {
pigment{ color rgb<1,1,1>*1.2}
finish { phong 0.5 } }
scale 0.5
} // end of parametric ----- |
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Conical spiral:
#declare a = 1.0;
#declare b = 8;
#declare c = 0.2;
#declare n = 5;
parametric{
function { a*(1-0.5*v/pi)*sin(n*v+0.5*pi)*(1-cos(u))
+ c*sin(n*v+0.5*pi) }
function { b*0.5*v/pi + a*(1-0.5*v/pi)*sin(u) }
function { a*(1-0.5*v/pi)*cos(n*v+0.5*pi)*(1-cos(u))
+ c*cos(n*v+0.5*pi) }
<0,0>,<2*pi,2*pi> // start, end of (u,v)
contained_by {box {<-1,-1,-1>*2*pi,<1,b/3,1>*2*pi}}
max_gradient 10
accuracy 0.0035
precompute 18 x,y,z
texture{ pigment{ color rgb<1,1,1>}
finish { phong 0.5}}
scale 0.125
rotate <0, 90, 0>
} // end of parametric ----- |
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Dini-Surface:
#declare a = 1;
#declare b = 0.2;
parametric{
function{ a*cos(u)*sin(v) } //x(u,v)
function{ cos(v)+ln(tan(v/2))+b*u } //y(u,v)
function{ a*sin(u)*sin(v) } //z(u,v)
<0,0.0001>,<4*pi,2> // start, end (u,v)
contained_by {box {<-1,-1,-1>*3,<1, 1, 1>*3}}
max_gradient 5
accuracy 0.0035
precompute 18 x,y,z
texture{
pigment{ color rgb<1,1,1>*1.2}
finish { phong 0.5 }}
scale 0.5
} // end of parametric ----- |
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