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Does there exist a freeware utility for converting bicubic patch objects to
triangle mesh objects? I have a few patches that I need to carry out CSG on,
the only way I can think of is by converting them to a mesh.
Also, is there any good tutorials on bicubic patches, that explain their
theory in an easy-to-grasp manner?
Dave
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jarbee wrote:
>
> Does there exist a freeware utility for converting bicubic patch objects to
> triangle mesh objects? I have a few patches that I need to carry out CSG on,
> the only way I can think of is by converting them to a mesh.
This macro takes the control points of a bicubic patch and creates the triangles.
Being recursive, it's slow. I used this to create the meshes for the Greb
characters in my IRTC entries. P0 through PF are the control points, and
Div is the number of times to divide.
#macro Bicubic(P0,P1,P2,P3,P4,P5,P6,P7,P8,P9,PA,PB,PC,PD,PE,PF,Div)
#if (Div<1)
smooth_triangle {
P0, vcross(P1-P0,P4-P0),
P3, vcross(P7-P3,P2-P3),
PF, vcross(PE-PF,PB-PF) }
smooth_triangle {
P0, vcross(P1-P0,P4-P0),
PF, vcross(PE-PF,PB-PF),
PC, vcross(P8-PC,PD-PC) }
#else
Bicubic(
P0,
(P0+P1)/2,
(P0+2*P1+P2)/4,
(P0+3*P1+3*P2+P3)/8,
(P0 + P4)/2,
(P0+P1 + P4+P5)/4,
(P0+2*P1+P2 + P4+2*P5+P6)/8,
(P0+3*P1+3*P2+P3 + P4+3*P5+3*P6+P7)/16,
(P0 + 2*P4 + P8)/4,
(P0+P1 + 2*P4+2*P5 + P8+P9)/8,
(P0+2*P1+P2 + 2*P4+4*P5+2*P6 + P8+2*P9+PA)/16,
(P0+3*P1+3*P2+P3 + 2*P4+6*P5+6*P6+2*P7 + P8+3*P9+3*PA+PB)/32,
(P0 + 3*P4 + 3*P8 + PC)/8,
(P0+P1 + 3*P4+3*P5 + 3*P8+3*P9 + PC+PD)/16,
(P0+2*P1+P2 + 3*P4+6*P5+3*P6 + 3*P8+6*P9+3*PA + PC+2*PD+PE)/32,
(P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB + PC+3*PD+3*PE+PF
)/64,
Div-1)
Bicubic(
(P0+3*P1+3*P2+P3)/8,
(P1+2*P2+P3)/4,
(P2+P3)/2,
P3,
( P0+3*P1+3*P2+P3 + P4+3*P5+3*P6+P7 )/16,
( P1+2*P2+P3 + P5+2*P6+P7 )/8,
( P2+P3 + P6+P7 )/4,
( P3 + P7 )/2,
( P0+3*P1+3*P2+P3 +2*P4+6*P5+6*P6+2*P7 + P8+3*P9+3*PA+PB)/32,
( P1+2*P2+P3 + 2*P5+4*P6+2*P7 + P9+2*PA+PB)/16,
( P2+P3 + 2*P6+2*P7 + PA+PB)/8,
( P3 + 2*P7 + PB)/4,
( P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB + PC+3*PD+3*PE+PF
)/64,
( P1+2*P2+P3 + 3*P5+6*P6+3*P7 + 3*P9+6*PA+3*PB + PD+2*PE+PF )/32,
( P2+P3 + 3*P6+3*P7 + 3*PA+3*PB + PE+PF )/16,
( P3 + 3*P7 + 3*PB + PF )/8,
Div-1)
Bicubic(
(P0 + 3*P4 + 3*P8 + PC)/8,
(P0+P1 + 3*P4+3*P5 + 3*P8+3*P9 + PC+PD)/16,
(P0+2*P1+P2 + 3*P4+6*P5+3*P6 + 3*P8+6*P9+3*PA + PC+2*PD+PE)/32,
(P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB + PC+3*PD+3*PE+PF
)/64,
( P4 + 2*P8 + PC )/4,
( P4+P5 + 2*P8+2*P9 + PC+PD )/8,
( P4+2*P5+P6 + 2*P8+4*P9+2*PA + PC+2*PD+PE)/16,
( P4+3*P5+3*P6+P7 + 2*P8+6*P9+6*PA+2*PB + PC+3*PD+3*PE+PF )/32,
( P8 + PC)/2,
( P8+P9 + PC+PD)/4,
( P8+2*P9+PA + PC+2*PD+PE)/8,
( P8+3*P9+3*PA+PB + PC+3*PD+3*PE+PF )/16,
PC,
( PC+PD)/2,
( PC+2*PD+PE)/4,
( PC+3*PD+3*PE+PF )/8,
Div-1)
Bicubic(
( P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB + PC+3*PD+3*PE+PF
)/64,
( P1+2*P2+P3 + 3*P5+6*P6+3*P7 + 3*P9+6*PA+3*PB + PD+2*PE+PF )/32,
( P2+P3 + 3*P6+3*P7 + 3*PA+3*PB + PE+PF )/16,
( P3 + 3*P7 + 3*PB + PF )/8,
( P4+3*P5+3*P6+P7 + 2*P8+6*P9+6*PA+2*PB + PC+3*PD+3*PE+PF )/32,
( P5+2*P6+P7 + 2*P9+4*PA+2*PB + PD+2*PE+PF )/16,
( P6+P7 + 2*PA+2*PB + PE+PF )/8,
( P7 + 2*PB + PF )/4,
( P8+3*P9+3*PA+PB + PC+3*PD+3*PE+PF )/16,
( P9+2*PA+PB + PD+2*PE+PF )/8,
( PA+PB + PE+PF )/4,
( PB + PF )/2,
( PC+3*PD+3*PE+PF )/8,
( PD+2*PE+PF )/4,
( PE+PF )/2,
( PF )/1,
Div-1)
#end
#end
Hope this helps,
John
--
ICQ: 46085459
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"John VanSickle" <van### [at] erols com> wrote in message
news:3AD772B7.C88CC3B0@erols.com...
>
> This macro takes the control points of a bicubic patch and creates the
triangles.
> Being recursive, it's slow. I used this to create the meshes for the Greb
> characters in my IRTC entries. P0 through PF are the control points, and
> Div is the number of times to divide.
>
> #macro Bicubic(P0,P1,P2,P3,P4,P5,P6,P7,P8,P9,PA,PB,PC,PD,PE,PF,Div)
> #if (Div<1)
> smooth_triangle {
> P0, vcross(P1-P0,P4-P0),
> P3, vcross(P7-P3,P2-P3),
> PF, vcross(PE-PF,PB-PF) }
> smooth_triangle {
> P0, vcross(P1-P0,P4-P0),
> PF, vcross(PE-PF,PB-PF),
> PC, vcross(P8-PC,PD-PC) }
> #else
> Bicubic(
> P0,
> (P0+P1)/2,
> (P0+2*P1+P2)/4,
> (P0+3*P1+3*P2+P3)/8,
>
> (P0 + P4)/2,
> (P0+P1 + P4+P5)/4,
> (P0+2*P1+P2 + P4+2*P5+P6)/8,
> (P0+3*P1+3*P2+P3 + P4+3*P5+3*P6+P7)/16,
>
> (P0 + 2*P4 + P8)/4,
> (P0+P1 + 2*P4+2*P5 + P8+P9)/8,
> (P0+2*P1+P2 + 2*P4+4*P5+2*P6 + P8+2*P9+PA)/16,
> (P0+3*P1+3*P2+P3 + 2*P4+6*P5+6*P6+2*P7 + P8+3*P9+3*PA+PB)/32,
>
> (P0 + 3*P4 + 3*P8 + PC)/8,
> (P0+P1 + 3*P4+3*P5 + 3*P8+3*P9 +
PC+PD)/16,
> (P0+2*P1+P2 + 3*P4+6*P5+3*P6 + 3*P8+6*P9+3*PA +
PC+2*PD+PE)/32,
> (P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB +
PC+3*PD+3*PE+PF )/64,
> Div-1)
>
> Bicubic(
> (P0+3*P1+3*P2+P3)/8,
> (P1+2*P2+P3)/4,
> (P2+P3)/2,
> P3,
>
> ( P0+3*P1+3*P2+P3 + P4+3*P5+3*P6+P7 )/16,
> ( P1+2*P2+P3 + P5+2*P6+P7 )/8,
> ( P2+P3 + P6+P7 )/4,
> ( P3 + P7 )/2,
>
> ( P0+3*P1+3*P2+P3 +2*P4+6*P5+6*P6+2*P7 + P8+3*P9+3*PA+PB)/32,
> ( P1+2*P2+P3 + 2*P5+4*P6+2*P7 + P9+2*PA+PB)/16,
> ( P2+P3 + 2*P6+2*P7 + PA+PB)/8,
> ( P3 + 2*P7 + PB)/4,
>
> ( P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB +
PC+3*PD+3*PE+PF )/64,
> ( P1+2*P2+P3 + 3*P5+6*P6+3*P7 + 3*P9+6*PA+3*PB +
PD+2*PE+PF )/32,
> ( P2+P3 + 3*P6+3*P7 + 3*PA+3*PB +
PE+PF )/16,
> ( P3 + 3*P7 + 3*PB +
PF )/8,
>
> Div-1)
>
> Bicubic(
> (P0 + 3*P4 + 3*P8 + PC)/8,
> (P0+P1 + 3*P4+3*P5 + 3*P8+3*P9 +
PC+PD)/16,
> (P0+2*P1+P2 + 3*P4+6*P5+3*P6 + 3*P8+6*P9+3*PA +
PC+2*PD+PE)/32,
> (P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB +
PC+3*PD+3*PE+PF )/64,
>
> ( P4 + 2*P8 + PC )/4,
> ( P4+P5 + 2*P8+2*P9 + PC+PD )/8,
> ( P4+2*P5+P6 + 2*P8+4*P9+2*PA + PC+2*PD+PE)/16,
> ( P4+3*P5+3*P6+P7 + 2*P8+6*P9+6*PA+2*PB + PC+3*PD+3*PE+PF )/32,
>
> ( P8 + PC)/2,
> ( P8+P9 + PC+PD)/4,
> ( P8+2*P9+PA + PC+2*PD+PE)/8,
> ( P8+3*P9+3*PA+PB + PC+3*PD+3*PE+PF )/16,
>
> PC,
> ( PC+PD)/2,
> ( PC+2*PD+PE)/4,
> ( PC+3*PD+3*PE+PF )/8,
> Div-1)
>
> Bicubic(
> ( P0+3*P1+3*P2+P3 + 3*P4+9*P5+9*P6+3*P7 + 3*P8+9*P9+9*PA+3*PB +
PC+3*PD+3*PE+PF )/64,
> ( P1+2*P2+P3 + 3*P5+6*P6+3*P7 + 3*P9+6*PA+3*PB +
PD+2*PE+PF )/32,
> ( P2+P3 + 3*P6+3*P7 + 3*PA+3*PB +
PE+PF )/16,
> ( P3 + 3*P7 + 3*PB +
PF )/8,
>
> ( P4+3*P5+3*P6+P7 + 2*P8+6*P9+6*PA+2*PB + PC+3*PD+3*PE+PF )/32,
> ( P5+2*P6+P7 + 2*P9+4*PA+2*PB + PD+2*PE+PF )/16,
> ( P6+P7 + 2*PA+2*PB + PE+PF )/8,
> ( P7 + 2*PB + PF )/4,
>
> ( P8+3*P9+3*PA+PB + PC+3*PD+3*PE+PF )/16,
> ( P9+2*PA+PB + PD+2*PE+PF )/8,
> ( PA+PB + PE+PF )/4,
> ( PB + PF )/2,
>
> ( PC+3*PD+3*PE+PF )/8,
> ( PD+2*PE+PF )/4,
> ( PE+PF )/2,
> ( PF )/1,
> Div-1)
>
> #end
> #end
>
I think that's what I needed, thanx. I've only tried it quickly so far, but
it seems to do a good job. I was thinking of incorporating it into a program
to do the conversions. Is that ok?
Dave
Post a reply to this message
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jarbee wrote:
>
> John VanSickle wrote:
>
> > This macro takes the control points of a bicubic patch and creates
> > the triangles.
> > Being recursive, it's slow. I used this to create the meshes for
> > the Greb characters in my IRTC entries. P0 through PF are the
> > control points, and Div is the number of times to divide.
<macro snipped>
> I think that's what I needed, thanx. I've only tried it quickly so
> far, but it seems to do a good job. I was thinking of incorporating it
> into a program to do the conversions. Is that ok?
Yeah, sure.
Regards,
John
--
ICQ: 46085459
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