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https://github.com/JustinSDK/dotSCAD.git
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added bijection_offset
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78
src/bijection_offset.scad
Normal file
78
src/bijection_offset.scad
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@@ -0,0 +1,78 @@
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function _bijection_edges_from(pts) =
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let(leng = len(pts))
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concat(
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[for(i = [0:leng - 2]) [pts[i], pts[i + 1]]],
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[[pts[len(pts) - 1], pts[0]]]
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);
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// 往內的法向量
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function _bijection_inward_edge_normal(edge) =
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let(
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pt1 = edge[0],
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pt2 = edge[1],
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dx = pt2[0] - pt1[0],
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dy = pt2[1] - pt1[1],
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edge_leng = norm([dx, dy])
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)
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[-dy / edge_leng, dx / edge_leng];
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// 往外的法向量
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function _bijection_outward_edge_normal(edge) = -1 * _bijection_inward_edge_normal(edge);
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function _bijection_offset_edge(edge, dx, dy) =
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let(
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pt1 = edge[0],
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pt2 = edge[1],
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dxy = [dx, dy]
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)
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[pt1 + dxy, pt2 + dxy];
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function _bijection__bijection_offset_edges(edges, d) =
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[
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for(edge = edges)
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let(
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ow_normal = _bijection_outward_edge_normal(edge),
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dx = ow_normal[0] * d,
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dy = ow_normal[1] * d
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)
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_bijection_offset_edge(edge, dx, dy)
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];
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function _bijection__bijection__bijection_offset_edges_intersection(edge1, edge2) =
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let(
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den = (edge2[1][1] - edge2[0][1]) * (edge1[1][0] - edge1[0][0]) - (edge2[1][0] - edge2[0][0]) * (edge1[1][1] - edge1[0][1])
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)
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// when den is 0, they are parallel or conincident edges
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den == 0 ? [] : _bijection_offset__bijection__bijection__bijection_offset_edges_intersection_sub(edge1, edge2, den);
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function _bijection_offset__bijection__bijection__bijection_offset_edges_intersection_sub(edge1, edge2, den) =
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let(
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ua = ((edge2[1][0] - edge2[0][0]) * (edge1[0][1] - edge2[0][1]) - (edge2[1][1] - edge2[0][1]) * (edge1[0][0] - edge2[0][0])) / den
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)
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[
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edge1[0][0] + ua * (edge1[1][0] - edge1[0][0]),
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edge1[0][1] + ua * (edge1[1][1] - edge1[0][1])
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];
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function bijection_offset(pts, d) =
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let(
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es = _bijection_edges_from(pts),
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offset_es = _bijection__bijection_offset_edges(es, d),
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leng = len(offset_es),
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last_p = _bijection__bijection__bijection_offset_edges_intersection(offset_es[leng - 1], offset_es[0])
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)
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concat(
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[
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for(i = [0:leng - 2])
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let(
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this_edge = offset_es[i],
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next_edge = offset_es[i + 1],
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p = _bijection__bijection__bijection_offset_edges_intersection(this_edge, next_edge)
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)
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// p == p to avoid [nan, nan], because [nan, nan] != [nan, nan]
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if(p != [] && p == p) p
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],
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last_p != [] && last_p == last_p ? [last_p] : []
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);
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