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https://github.com/revarbat/BOSL2.git
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Added support for triangular bezier patches.
This commit is contained in:
Revar Desmera
parent
c244156be4
commit
b8239d2dde
235
beziers.scad
235
beziers.scad
@ -224,6 +224,31 @@ function fillet3pts(p0, p1, p2, r, maxerr=0.1, w=0.5, dw=0.25) = let(
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function bezier_patch_point(patch, u, v) = bez_point([for (bez = patch) bez_point(bez, u)], v);
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// Function: bezier_triangle_point()
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// Usage:
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// bezier_triangle_point(patch, u, v)
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// Description:
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// Given a triangular 2-dimensional array of N+1 by (for the first row) N+1 points,
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// that represents a Bezier triangular patch of degree N, returns a point on
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// that surface, at positions `u`, and `v`. A cubic bezier triangular patch
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// will have a list of 4 points in the first row, 3 in the second, 2 in the
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// third, and 1 in the last row.
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// Arguments:
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// patch = Triangular bezier patch to get point on.
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// u = The proportion of the way along the first dimension of the triangular patch to find the point of. 0<=`u`<=1
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// v = The proportion of the way along the second dimension of the triangular patch to find the point of. 0<=`v`<=(1-`u`)
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function bezier_triangle_point(patch, u, v) =
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len(patch) == 1 ? patch[0][0] :
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let(
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n = len(patch)-1,
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Pu = [for(i=[0:n-1]) select(patch[i],1,-1)],
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Pv = [for(i=[0:n-1]) select(patch[i],0,-2)],
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Pw = select(patch,1,-1)
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)
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bezier_triangle_point(u*Pu + v*Pv + (1-u-v)*Pw, u, v);
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// Internal, not exposed.
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function _vertex_list_merge(v1, v2) = concat(v1, [for (v=v2) if (!in_list(v,v1)) v]);
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function _vertex_list_face(v, face) = [for (pt = face) search([pt], v, num_returns_per_match=1)[0]];
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@ -233,13 +258,15 @@ function _vertex_list_face(v, face) = [for (pt = face) search([pt], v, num_retur
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// Usage:
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// bezier_patch_vertices_and_faces(patch, [splinesteps], [vertices], [faces]);
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// Description:
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// Calculate vertices and faces for forming a partial polyhedron from the given bezier patch.
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// Returns a list containing two elements. The first is the list of unique vertices.
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// The second is the list of faces, where each face is a list of indices into the
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// list of vertices. You can chain calls to this, to add more vertices and faces
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// for multiple bezier patches, to stitch them together into a complete polyhedron.
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// Calculate vertices and faces for forming a partial polyhedron
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// from the given bezier rectangular patch. Returns a list containing
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// two elements. The first is the list of unique vertices. The
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// second is the list of faces, where each face is a list of indices
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// into the list of vertices. You can chain calls to this, to add
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// more vertices and faces for multiple bezier patches, to stitch
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// them together into a complete polyhedron.
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// Arguments:
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// patch = The 2D array of endpoints and control points for this bezier patch.
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// patch = The rectangular array of endpoints and control points for this bezier patch.
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// splinesteps = Number of steps to divide each bezier segment into. Default: 16
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// vertices = Vertex list to add new points to. Default: []
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// faces = Face list to add new faces to. Default: []
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@ -264,18 +291,152 @@ function bezier_patch_vertices_and_faces(patch, splinesteps=16, vertices=[], fac
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) [new_vertices, concat(faces, new_faces)];
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// Function: bezier_triangle_vertices_and_faces()
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// Usage:
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// bezier_triangle_vertices_and_faces(patch, [splinesteps], [vertices], [faces]);
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// Description:
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// Calculate vertices and faces for forming a partial polyhedron
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// from the given bezier triangular patch. Returns a list containing
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// two elements. The first is the list of unique vertices. The
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// second is the list of faces, where each face is a list of indices
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// into the list of vertices. You can chain calls to this, to add
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// more vertices and faces for multiple bezier patches, to stitch
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// them together into a complete polyhedron.
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// Arguments:
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// patch = The triangular array of endpoints and control points for this bezier patch.
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// splinesteps = Number of steps to divide each bezier segment into. Default: 16
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// vertices = Vertex list to add new points to. Default: []
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// faces = Face list to add new faces to. Default: []
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function bezier_triangle_vertices_and_faces(patch, splinesteps=16, vertices=[], faces=[]) =
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let(
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pts = [for (u=[0:splinesteps], v=[0:splinesteps-u]) bezier_triangle_point(patch, u/splinesteps, v/splinesteps)],
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new_vertices = _vertex_list_merge(vertices, pts),
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new_faces = [
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for (
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u=[0:splinesteps-1],
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v=[0:splinesteps-u-1]
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) let (
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v1 = bezier_triangle_point(patch, u/splinesteps, v/splinesteps),
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v2 = bezier_triangle_point(patch, (u+1)/splinesteps, v/splinesteps),
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v3 = bezier_triangle_point(patch, u/splinesteps, (v+1)/splinesteps),
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v4 = bezier_triangle_point(patch, (u+1)/splinesteps, (v+1)/splinesteps),
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allfaces = concat(
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[[v1,v2,v3]],
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((u<splinesteps-1 && v<splinesteps-u-1)? [[v2,v4,v3]] : [])
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)
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) for (facepts=allfaces) _vertex_list_face(new_vertices, facepts)
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]
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) [new_vertices, concat(faces, new_faces)];
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// Function: bezier_patch_flat()
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// Usage:
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// bezier_patch_flat(size, [N], [orient], [trans]);
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// Description:
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// Returns a flat rectangular bezier patch of degree `N`, centered on the XY plane.
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// Arguments:
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// size = 2D XY size of the patch.
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// N = Degree of the patch to generate. Since this is flat, a degree of 1 should usually be sufficient.
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// orient = The orientation to rotate the edge patch into. Use the `ORIENT` constants in `BOSL/constants.scad`.
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// trans = Amount to translate patch, after rotating to `orient`.
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function bezier_patch_flat(size=[100,100], N=4, orient=ORIENT_Z, trans=[0,0,0]) =
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let(
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patch = [for (x=[0:N]) [for (y=[0:N]) vmul(point3d(size),[x/N-0.5, 0.5-y/N, 0])]]
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) [for (row=patch)
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translate_points(v=trans,
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rotate_points3d(v=orient,row)
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)
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];
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// Function: patch_translate()
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// Usage:
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// patch_translate(patch, v)
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// Description: Translates all coordinates in a rectangular or triangular patch by a given amount.
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// Arguments:
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// patch = The patch to translate.
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// v = Vector to translate by.
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function patch_translate(patch, v=[0,0,0]) = [for(row=patch) translate_points(row, v)];
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// Function: patch_scale()
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// Usage:
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// patch_scale(patch, v, [cp])
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// Description: Scales all coordinates in a rectangular or triangular patch by a given amount.
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// Arguments:
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// patch = The patch to scale.
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// v = [X,Y,Z] scaling factors.
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// cp = Centerpoint to scale around.
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function patch_scale(patch, v=[1,1,1], cp=[0,0,0]) = [for(row=patch) scale_points(row, v, cp)];
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// Function: patch_rotate()
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// Usage:
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// patch_rotate(patch, a, [cp])
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// patch_rotate(patch, a, v, [cp])
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// Description: Rotates all coordinates in a rectangular or triangular patch by a given amount.
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// Arguments:
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// patch = The patch to rotate.
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// a = Rotation angle(s) in degrees.
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// v = Vector axis to rotate round.
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// cp = Centerpoint to rotate around.
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function patch_rotate(patch, a=undef, v=undef, cp=[0,0,0]) =
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v==undef?
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[for(row=patch) rotate_points3d(row, a, cp)] :
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[for(row=patch) rotate_points3d_around_axis(row, a, v, cp)];
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// Function: patches_translate()
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// Usage:
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// patches_translate(patch, v, [cp])
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// Description: Translates all coordinates in each of a list of rectangular or triangular patches.
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// Arguments:
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// patches = List of patches to translate.
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// v = Vector to translate by.
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function patches_translate(patches, v=[0,0,0]) = [for (patch=patches) patch_translate(patch,v)];
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// Function: patches_scale()
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// Usage:
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// patches_scale(patch, v, [cp])
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// Description: Scales all coordinates in each of a list of rectangular or triangular patches.
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// Arguments:
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// patches = List of patches to scale.
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// v = [X,Y,Z] scaling factors.
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// cp = Centerpoint to scale around.
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function patches_scale(patches, v=[1,1,1], cp=[0,0,0]) = [for (patch=patches) patch_scale(patch,v,cp)];
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// Function: patches_rotate()
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// Usage:
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// patches_rotate(patch, a, [cp])
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// patches_rotate(patch, a, v, [cp])
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// Description: Rotates all coordinates in each of a list of rectangular or triangular patches.
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// Arguments:
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// patches = List of patches to rotate.
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// a = Rotation angle(s) in degrees.
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// v = Vector axis to rotate round.
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// cp = Centerpoint to rotate around.
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function patches_rotate(patches, a=undef, v=undef, cp=[0,0,0]) = [for (patch=patches) patch_rotate(patch, a=a, v=v, cp=cp)];
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// Function: bezier_surface_vertices_and_faces()
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// Usage:
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// bezier_surface_vertices_and_faces(patches, [splinesteps], [vertices], [faces]);
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// Description:
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// Calculate vertices and faces for forming a (possibly partial) polyhedron from the given bezier patches.
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// Returns a list containing two elements. The first is the list of unique vertices.
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// The second is the list of faces, where each face is a list of indices into the
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// list of vertices. You can chain calls to this, to add more vertices and faces
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// for multiple bezier patches, to stitch them together into a complete polyhedron.
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// Calculate vertices and faces for forming a (possibly partial)
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// polyhedron from the given rectangular and triangular bezier
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// patches. Returns a list containing two elements. The first is
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// the list of unique vertices. The second is the list of faces,
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// where each face is a list of indices into the list of vertices.
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// You can chain calls to this, to add more vertices and faces for
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// multiple bezier patches, to stitch them together into a complete
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// polyhedron.
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// Arguments:
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// patches = A list of bezier patches.
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// patches = A list of rectangular bezier patches.
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// tripatches = A list of triangular bezier patches.
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// splinesteps = Number of steps to divide each bezier segment into. Default: 16
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// vertices = Vertex list to add new points to. Default: []
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// faces = Face list to add new faces to. Default: []
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@ -292,13 +453,16 @@ function bezier_patch_vertices_and_faces(patch, splinesteps=16, vertices=[], fac
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// [[ 0,60,0], [ 0,100,-50], [100,100,-50], [100, 60,0]],
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// [[18,82,0], [33,100, 0], [ 67,100, 0], [ 82, 82,0]],
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// ];
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// vnf = bezier_surface_vertices_and_faces([patch1, patch2], splinesteps=16);
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// vnf = bezier_surface_vertices_and_faces(patches=[patch1, patch2], splinesteps=16);
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// polyhedron(points=vnf[0], faces=vnf[1]);
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function bezier_surface_vertices_and_faces(patches, splinesteps=16, i=0, vertices=[], faces=[]) =
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function bezier_surface_vertices_and_faces(patches=[], tripatches=[], splinesteps=16, i=0, vertices=[], faces=[]) =
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let(
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vnf = bezier_patch_vertices_and_faces(patches[i], splinesteps=splinesteps, vertices=vertices, faces=faces)
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) i >= len(patches)? vnf :
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bezier_surface_vertices_and_faces(patches, splinesteps=splinesteps, i=i+1, vertices=vnf[0], faces=vnf[1]);
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vnf = (i >= len(patches))? [vertices, faces] :
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bezier_patch_vertices_and_faces(patches[i], splinesteps=splinesteps, vertices=vertices, faces=faces),
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vnf2 = (i >= len(tripatches))? vnf :
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bezier_triangle_vertices_and_faces(tripatches[i], splinesteps=splinesteps, vertices=vnf[0], faces=vnf[1])
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) (i >= len(patches) && i >= len(tripatches))? vnf2 :
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bezier_surface_vertices_and_faces(patches=patches, tripatches=tripatches, splinesteps=splinesteps, i=i+1, vertices=vnf2[0], faces=vnf2[1]);
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@ -334,7 +498,6 @@ function bezier_path_point(path, seg, u, N=3) = bez_point(select(path,seg*N,(seg
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// bez = [[0,0], [20,40], [60,-25], [80,0], [100,25], [140,25], [160,0]];
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// pos = bezier_path_closest_point(bez, pt);
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// xy = bezier_path_point(bez,pos[0],pos[1]);
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// echo(pos=pos);
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// trace_bezier(bez, N=3);
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// color("red") translate(pt) sphere(r=1);
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// color("blue") translate(xy) sphere(r=1);
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@ -762,7 +925,10 @@ module trace_bezier(bez, N=3, size=1) {
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// Description:
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// Takes a list of two or more bezier patches and attempts to make a complete polyhedron from them.
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// Arguments:
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// patches = A list of bezier patches.
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// patches = A list of rectangular bezier patches.
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// tripatches = A list of triangular bezier patches.
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// vertices = Vertex list for additional non-bezier faces. Default: []
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// faces = Additional non-bezier faces. Default: []
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// splinesteps = Number of steps to divide each bezier segment into. Default: 16
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// Example:
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// patch1 = [
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@ -778,9 +944,9 @@ module trace_bezier(bez, N=3, size=1) {
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// [[18,82,0], [33,100, 0], [ 67,100, 0], [ 82, 82,0]],
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// ];
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// bezier_polyhedron([patch1, patch2], splinesteps=8);
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module bezier_polyhedron(patches, splinesteps=16)
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module bezier_polyhedron(patches=[], tripatches=[], splinesteps=16, vertices=[], faces=[])
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{
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sfc = bezier_surface_vertices_and_faces(patches, splinesteps=splinesteps);
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sfc = bezier_surface_vertices_and_faces(patches=patches, tripatches=tripatches, splinesteps=splinesteps, vertices=vertices, faces=faces);
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polyhedron(points=sfc[0], faces=sfc[1]);
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}
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@ -789,10 +955,13 @@ module bezier_polyhedron(patches, splinesteps=16)
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// Module: trace_bezier_patches()
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// Usage:
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// trace_bezier_patches(patches, [size], [showcps], [splinesteps]);
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// trace_bezier_patches(tripatches, [size], [showcps], [splinesteps]);
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// trace_bezier_patches(patches, tripatches, [size], [showcps], [splinesteps]);
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// Description:
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// Shows the surface, and optionally, control points of a list of bezier patches.
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// Arguments:
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// patches = A list of bezier patches.
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// patches = A list of rectangular bezier patches.
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// tripatches = A list of triangular bezier patches.
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// splinesteps = Number of steps to divide each bezier segment into. default=16
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// showcps = If true, show the controlpoints as well as the surface.
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// size = Size to show control points and lines.
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@ -809,21 +978,31 @@ module bezier_polyhedron(patches, splinesteps=16)
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// [[ 0,67,0], [33, 67,-50], [ 67, 67,-50], [100, 67,0]],
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// [[15,85,0], [33,100, 0], [ 67,100, 0], [ 85, 85,0]],
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// ];
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// trace_bezier_patches([patch1, patch2], splinesteps=8, showcps=true);
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module trace_bezier_patches(patches, size=1, showcps=false, splinesteps=16)
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// trace_bezier_patches(patches=[patch1, patch2], splinesteps=8, showcps=true);
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module trace_bezier_patches(patches=[], tripatches=[], size=1, showcps=false, splinesteps=16)
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{
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for (patch = patches) {
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if (showcps) {
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if (showcps) {
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for (patch = patches) {
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place_copies(flatten(patch)) color("red") sphere(d=size*2);
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color("cyan")
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for (i=[0:len(patch)-1], j=[0:len(patch[i])-1]) {
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if (i<len(patch)-1) extrude_from_to(patch[i][j], patch[i+1][j]) circle(d=size);
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if (j<len(patch[i])-1) extrude_from_to(patch[i][j], patch[i][j+1]) circle(d=size);
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}
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vnf = bezier_patch_vertices_and_faces(patch, splinesteps=splinesteps);
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place_copies(vnf[0]) color("blue") sphere(d=size);
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}
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for (patch = tripatches) {
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place_copies(flatten(patch)) color("red") sphere(d=size*2);
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color("cyan")
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for (i=[0:len(patch)-2], j=[0:len(patch[i])-2]) {
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extrude_from_to(patch[i][j], patch[i+1][j]) circle(d=size);
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extrude_from_to(patch[i][j], patch[i][j+1]) circle(d=size);
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extrude_from_to(patch[i+1][j], patch[i][j+1]) circle(d=size);
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}
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vnf = bezier_triangle_vertices_and_faces(patch, splinesteps=splinesteps);
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}
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}
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bezier_polyhedron(patches, splinesteps=splinesteps);
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bezier_polyhedron(patches=patches, tripatches=tripatches, splinesteps=splinesteps);
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}
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