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Merge pull request #859 from adrianVmariano/master

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bezier examples
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Revar Desmera 2022-04-27 14:36:09 -07:00 committed by GitHub
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@ -1297,18 +1297,85 @@ function bezier_vnf_degenerate_patch(patch, splinesteps=16, reverse=false, retur
// Topics: Bezier Patches
// See Also: bezier_patch_points(), bezier_points(), bezier_curve(), bezpath_curve()
// Description:
// Compute the normal vector to a bezier patch at the listed point set. The bezier patch must be a rectangular array of
// Compute the unit normal vector to a bezier patch at the listed point set. The bezier patch must be a rectangular array of
// points, and the normal will be computed at all the (u,v) pairs that you specify. If you give u and v
// as single numbers you'll get a single point back. If you give u and v as lists or ranges you'll
// get a 2d rectangular array of points. If one but not both of u and v is a list or range then you'll
// get a list of points.
// .
// This function works by computing the cross product of the tangents. If the tangents are parallel, or nearly parallel, the result
// will be invalid. This can happen if you use a degenerate patch, or if you give two of the edges of your patch a smooth corner.
// This function works by computing the cross product of the tangents. In some degenerate cases the one of the tangents
// can be zero, so the normal vector does not exist. In this case, undef is returned. Another degenerate case
// occurs when the tangents are parallel, or nearly parallel. In this case you will get a unit vector returned but it will not
// be the correct normal vector. This can happen if you use a degenerate patch, or if you give two of the edges of your patch a smooth "corner"
// so that the u and v directions are parallel at the corner.
// Arguments:
// patch = The 2D array of control points for a Bezier patch.
// u = The bezier u parameter (inner list of patch). Generally between 0 and 1. Can be a list, range or value.
// v = The bezier v parameter (outer list of patch). Generally between 0 and 1. Can be a list, range or value.
// Example(3D,Med,VPR=[71.1,0,155.9],VPD=292.705,VPT=[20.4724,38.7273,22.7683],NoAxes): Normal vectors on a patch
// patch = [
// // u=0,v=0 u=1,v=0
// [[-50,-50, 0], [-16,-50, 20], [ 16,-50, -20], [50,-50, 0]],
// [[-50,-16, 40], [-16,-16, 20], [ 16,-16, -20], [50,-16, 70]],
// [[-50, 16, 20], [-16, 16, -20], [ 16, 37, 20], [70, 16, 20]],
// [[-50, 50, 0], [73, 50, -40], [ 16, 50, 20], [50, 50, 0]],
// // u=0,v=1 u=1,v=1
// ];
// vnf_polyhedron(bezier_vnf(patch,splinesteps=30));
// uv = lerpn(0,1,12);
// pts = bezier_patch_points(patch, uv, uv);
// normals = bezier_patch_normals(patch, uv, uv);
// for(i=idx(uv),j=idx(uv)){
// stroke([pts[i][j],pts[i][j]-6*normals[i][j]], width=0.5,
// endcap1="dot",endcap2="arrow2",color="blue");
// }
// Example(3D,NoAxes,Med,VPR=[72.5,0,288.9],VPD=192.044,VPT=[51.6089,48.118,5.89088]): This example gives invalid normal vectors at the four corners of the patch where the u and v directions are parallel. You can see how the line of triangulation is approaching parallel at the edge, and the invalid vectors in red point in a completely incorrect direction.
// patch = [
// [[18,18,0], [33, 0, 0], [ 67, 0, 0], [ 82, 18,0]],
// [[ 0,40,0], [ 0, 0,100], [100, 0, 20], [100, 40,0]],
// [[ 0,60,0], [ 0,100,100], [100,100, 20], [100, 60,0]],
// [[18,82,0], [33,100, 0], [ 67,100, 0], [ 82, 82,0]],
// ];
// vnf_polyhedron(bezier_vnf(patch,splinesteps=30));
// uv = lerpn(0,1,7);
// pts = bezier_patch_points(patch, uv, uv);
// normals = bezier_patch_normals(patch, uv, uv);
// for(i=idx(uv),j=idx(uv)){
// color=((uv[i]==0 || uv[i]==1) && (uv[j]==0 || uv[j]==1))
// ? "red" : "blue";
// stroke([pts[i][j],pts[i][j]-8*normals[i][j]], width=0.5,
// endcap1="dot",endcap2="arrow2",color=color);
// }
// Example(3D,Med,NoAxes,VPR=[56.4,0,71.9],VPD=66.9616,VPT=[10.2954,1.33721,19.4484]): This degenerate patch has normals everywhere, but computational of the normal fails at the point of degeneracy, the top corner.
// patch=[
// repeat([-12.5, 12.5, 15],5),
// [[-6.25, 11.25, 15], [-6.25, 8.75, 15], [-6.25, 6.25, 15], [-8.75, 6.25, 15], [-11.25, 6.25, 15]],
// [[0, 10, 15], [0, 5, 15], [0, 0, 15], [-5, 0, 15], [-10, 0, 15]],
// [[0, 10, 8.75], [0, 5, 8.75], [0, 0, 8.75], [-5, 0, 8.75], [-10, 0, 8.75]],
// [[0, 10, 2.5], [0, 5, 2.5], [0, 0, 2.5], [-5, 0, 2.5], [-10, 0, 2.5]]
// ];
// vnf_polyhedron(bezier_vnf(patch, 32));
// uv = lerpn(0,1,8);
// pts = bezier_patch_points(patch, uv, uv);
// normals = bezier_patch_normals(patch, uv, uv);
// for(i=idx(uv),j=idx(uv)){
// if (is_def(normals[i][j]))
// stroke([pts[i][j],pts[i][j]-2*normals[i][j]], width=0.1,
// endcap1="dot",endcap2="arrow2",color="blue");
// }
// Example(3D,Med,NoAxes,VPR=[48,0,23.6],VPD=32.0275,VPT=[-0.145727,-0.0532125,1.74224]): This example has a singularities where the tangent lines don't exist, so the normal will be undef at those points.
// pts1 = [ [-5,0,0], [5,0,5], [-5,0,5], [5,0,0] ];
// pts2 = [ [0,-5,0], [0,5,5], [0,-5,5], [0,5,0] ];
// patch = [for(i=[0:3])
// [for(j=[0:3]) pts1[i]+pts2[j] ] ];
// vnf_polyhedron(bezier_vnf(patch, 163));
// uv = [0,.1,.2,.3,,.7,.8,.9,1];//lerpn(0,1,8);
// pts = bezier_patch_points(patch, uv, uv);
// normals = bezier_patch_normals(patch, uv, uv);
// for(i=idx(uv),j=idx(uv))
// stroke([pts[i][j],pts[i][j]+2*normals[i][j]], width=0.08,
// endcap1="dot",endcap2="arrow2",color="blue");
function bezier_patch_normals(patch, u, v) =
assert(is_range(u) || is_vector(u) || is_finite(u), "Input u is invalid")
assert(is_range(v) || is_vector(v) || is_finite(v), "Input v is invalid")
@ -1319,13 +1386,13 @@ function bezier_patch_normals(patch, u, v) =
v_tangent = [for (i = idx(vbezes[0])) bezier_derivative(column(vbezes,i), v)],
u_tangent = [for (i = idx(vbezes[0])) bezier_points(column(dvbezes,i), v)]
)
[for(i=idx(u_tangent)) [for(j=idx(u_tangent[0])) unit(cross(u_tangent[i][j],v_tangent[i][j]))]]
[for(i=idx(u_tangent)) [for(j=idx(u_tangent[0])) unit(cross(u_tangent[i][j],v_tangent[i][j]),undef)]]
: is_num(u) && is_num(v)?
let(
du = bezier_derivative([for (bez = patch) bezier_points(bez, v)], u),
dv = bezier_points([for (bez = patch) bezier_derivative(bez, v)], u)
)
unit(cross(du,dv))
unit(cross(du,dv),undef)
: is_num(u) ? bezier_patch_normals(patch,force_list(u),v)[0]
: column(bezier_patch_normals(patch,u,force_list(v)),0);