added bijection_offset

src/bijection_offset.scad

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