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"Bald Eagle" <cre### [at] netscape net> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>
> > I ran all these through the SimpleMesh macro. See the attached image for
> > the results. I can post the complete source for that if you're interested.
>
> Yes, that would be interesting to look over.
> ...
Here's the code:
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
#version 3.7;
global_settings { assumed_gamma 1.0 }
#include "functions.inc" // For f_r()
#include "colors.inc"
#declare TAU = 2*pi;
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
#macro SimpleMesh(FnX, FnY, FnZ, MinU, MaxU, MinV, MaxV, SizeI, SizeJ)
#local LastI = SizeI - 1;
#local LastJ = SizeJ - 1;
#local Vertices = array[SizeI][SizeJ];
#local SpanU = MaxU - MinU;
#local SpanV = MaxV - MinV;
#for (I, 0, LastI)
#local U = MinU + I/LastI*SpanU;
#for (J, 0, LastJ)
#local V = MinV + J/LastJ*SpanV;
#local Vertices[I][J] =
<FnX(U, V), FnY(U, V), FnZ(U, V)>
;
#end // for
#end // for
mesh {
#for (I, 0, LastI - 1)
#for (J, 0, LastJ - 1)
#local p00 = Vertices[I ][J ];
#local p01 = Vertices[I ][J+1];
#local p10 = Vertices[I+1][J ];
#local p11 = Vertices[I+1][J+1];
triangle { p00, p10, p11 }
triangle { p11, p01, p00 }
#end // for
#end // for
}
#end // macro SimpleMesh
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
#declare FnX = function(u) { u };
#declare DFnX = function(u) { 1 };
#declare Fn_Y = array[5];
#declare DFn_Y = array[5];
#declare I = 0;
#declare Fn_Y[I] = function(u) { pow(u, 2) + 1 };
#declare DFn_Y[I] = function(u) { 2*u };
#declare I = I + 1;
#declare Fn_Y[I] = function(u) { 0.4*cos(u)*(-pow(u, 2) + 3) - 1 };
#declare DFn_Y[I] = function(u) { 0.4*(pow(u, 2) - 3)*sin(u) - 0.8*u*cos(u) };
#declare I = I + 1;
#declare Fn_Y[I] = function(u) { u*u*u };
#declare DFn_Y[I] = function(u) { 3*u*u };
#declare I = I + 1;
#declare Fn_Y[I] = function(u) { 4*sinh(u)/cosh(u) + 4 };
#declare DFn_Y[I] = function(u) { 16*pow(cosh(u), 2)/pow(cosh(2*u) + 1, 2) };
#declare I = I + 1;
#declare Fn_Y[I] = function(u) { 8*u/(abs(u) + 1) };
#declare DFn_Y[I] = function(u) { 8/pow(abs(u) + 1, 2) };
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
#declare Nil = 1e-3;
#declare R = 0.15;
#declare Colors =
array[5] {
color Red,
color Green,
color Blue,
// color Cyan,
color Magenta,
color Yellow
}
;
#for (I, 0, 4)
#declare FnY = Fn_Y[I];
#declare DFnY = DFn_Y[I];
// Normalized component functions for tangent vector
#declare N_DFnX =
function(u) {
DFnX(u)/f_r(DFnX(u), DFnY(u), 0)
}
;
#declare N_DFnY =
function(u) {
DFnY(u)/f_r(DFnX(u), DFnY(u), 0)
}
;
object {
SimpleMesh(
function(u, v) { -R*cos(v)*N_DFnY(u) + FnX(u) }, // FnX
function(u, v) { +R*cos(v)*N_DFnX(u) + FnY(u) }, // FnY
function(u, v) { R*sin(v) }, // FnZ
-20, +20, // MinU, MaxU,
0 + Nil, TAU - Nil, // MinV, MaxV
800 + 1, 26 + 1 // SizeI, Size J
)
pigment { color Gray50 + Colors[I] }
}
#undef FnY
#undef DFnY
#undef N_DFnX
#undef N_DFnY
#end // for
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
background { color rgb <0.04, 0.02, 0.06> }
light_source {
-150*z
color White
shadowless
}
#declare AR = image_width/image_height;
camera {
orthographic
location -85*z + 0.5*y
direction z
right AR*x
up y
sky y
angle 15
}
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
(Note that the colors are more saturated than in the image I posted.)
--
Tor Olav
http://subcube.com
https://github.com/t-o-k
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