"Tim Attwood" <tim### [at] comcastnet> wrote:
> Given three points you can define a plane, so if you take three
> close together points from a path you can find the tangent.
> Once you have the tangent, you can take a tangent point, and
> two points from the path to define a plane that has a normal
> in the direction of curve.
>
> This should work in most situations, but may have odd behavior
> along a straight line. You may also need to check the direction
> of the normal and reverse it if the curve is flipped, though this
> sample doesn't seem to misbehave without that sort of check.
>
> #include "colors.inc"
> #include "math.inc"
> #include "transforms.inc"
>
> #default {finish{ambient 0.7}}
> // --- camera, lights &
> background ------------------------------------------
> camera {
>    location  <0.0, 1, -4.0>
>    direction 1.5*z
>    right     x*image_width/image_height
>    look_at   <0.0, 0.5,  0.0>
> }
>
> background {Gray85}
>
> light_source {
>   <-30, 30, -30>
>   color rgb <1, 1, 1>
> }
>
> // ---
> macros ---------------------------------------------------------------
> #declare Path_Spline = spline {
>    natural_spline
>    0, <-2,0,0>
>    1, <-1,0,0>
>    2, <-0.5,0.5,0>
>    3, <0,1,1>
>    4, <0.5,0.5,0>
>    5, <1,0,0>
>    6, <2,0,0>
> };
>
> #macro Path_Normal(N, rez)
>    #local P1 = Path_Spline(N-rez);
>    #local P2 = Path_Spline(N);
>    #local P3 = Path_Spline(N+rez);
>    #local HPerp = VPerp_To_Plane(vnormalize(P2-P1),vnormalize(P3-P2));
>    #local Perp = VPerp_To_Plane(vnormalize(HPerp-P2),vnormalize(P3-P2));
>    (Perp)
> #end
>
> // show spline
> #local C = 0;
> #while (C <= 6)
>    sphere{Path_Spline(C),0.01 pigment {Yellow}}
>    #local C=C+0.005;
> #end
>
> // inside of curve
> #local C = 0.5;
> #while (C <= 5.5)
>    #local Perp = Path_Normal(C,0.1);
>    sphere {Path_Spline(C)+Perp/10,0.01 pigment{Orange}}
>    #local C=C+0.005;
> #end

Thanks, Tim.
While I agree with your code, I'm a bit puzzled by the results.
I changed point 3 of the spline to <0,1,0>, so that the spline lies in the Z=0
plane.
First observation: if the spline lies in the Z=0 plane, so should the orange
locus, but it doesn't. I don't know why.
OTOH the orange curve is discontinuous where you expect it, i.e. at the
inflection points of the spline.

I also would write (P3-P1) instead of (P3-P2) in the calculation of Perp, but
since P1, P2 and P3 are nearly collinear this shouldn't make much difference
(and it doesn't).

Thanks again.
Steven

(Learned this lesson: "VPerp_To_Plane" :-))

Post a reply to this message