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+// a function to round sharp edges of open and cyclic paths
+// written by stefan knorr
+
+path roundedpath(path A, real R, real S = 1)
+// create rounded path from path A with radius R and scale S = 1
+{
+ path RoundPath; // returned path
+ path LocalPath; // local straight subpath
+ path LocalCirc; // local edge circle for intersection
+ real LocalTime; // local intersectiontime between . and ..
+ pair LocalPair; // local point to be added to 'RoundPath'
+
+ int len=length(A); // length of given path 'A'
+ bool PathClosed=cyclic(A); // true, if given path 'A' is cyclic
+
+ // initialisation: define first Point of 'RoundPath' as
+ if (PathClosed) // ? is 'A' cyclic
+ RoundPath=scale(S)*point(point(A,0)--point(A,1), 0.5); // centerpoint of first straight subpath of 'A'
+ else
+ RoundPath=scale(S)*point(A,0); // first point of 'A'
+
+ // doing everything between start and end
+ // create round paths subpath by subpath for every i-th edge
+ for(int i=1; i < len; ++i)
+ {
+ // straight subpath towards i-th edge
+ LocalPath=point(A,i-1)---point(A,i);
+ // circle with radius 'R' around i-th edge
+ LocalCirc=circle(point(A,i),R);
+ // calculate intersection time between straight subpath and circle
+ real[] t=intersect(LocalPath, LocalCirc);
+ if(t.length > 0) {
+ LocalTime=t[0];
+ // define intersectionpoint between both paths
+ LocalPair=point(subpath(LocalPath, 0, LocalTime), 1);
+ // add straight subpath towards i-th curvature to 'RoundPath'
+ RoundPath=RoundPath--scale(S)*LocalPair;
+ }
+
+ // straight subpath from i-th edge to (i+1)-th edge
+ LocalPath=point(A,i)---point(A,i+1);
+ // calculate intersection-time between straight subpath and circle
+ real[] t=intersect(LocalPath, LocalCirc);
+ if(t.length > 0) {
+ LocalTime=t[0];
+ // define intersectionpoint between both paths
+ LocalPair=point(subpath(LocalPath, 0, LocalTime), 1);
+ // add curvature near i-th edge to 'RoundPath'
+ RoundPath=RoundPath..scale(S)*LocalPair;
+ }
+ }
+
+ // final steps to have a correct termination
+ if(PathClosed) { // Is 'A' cyclic?
+ // straight subpath towards 0-th edge
+ LocalPath=point(A,len-1)---point(A,0);
+ // circle with radius 'R' around 0-th edge
+ LocalCirc=circle(point(A,0),R);
+ // calculate intersection-time between straight subpath and circle
+ real[] t=intersect(LocalPath, LocalCirc);
+ if(t.length > 0) {
+ LocalTime=t[0];
+ // define intersectionpoint between both paths
+ LocalPair=point(subpath(LocalPath, 0, LocalTime), 1);
+ // add straight subpath towards 0-th curvature to 'RoundPath'
+ RoundPath=RoundPath--scale(S)*LocalPair;
+ }
+
+
+ // straight subpath from 0-th edge to 1st edge
+ LocalPath=point(A,0)---point(A,1);
+ // calculate intersection-time between straight subpath and circle
+ real[] t=intersect(LocalPath, LocalCirc);
+ if(t.length > 0) {
+ LocalTime=t[0];
+ // define intersectionpoint between both paths
+ LocalPair=point(subpath(LocalPath, 0, LocalTime), 1);
+ // add curvature near 0-th edge to 'RoundPath' and close path
+ RoundPath=RoundPath..scale(S)*LocalPair--cycle;
+ }
+ } else
+ RoundPath=RoundPath--scale(S)*point(A,len);
+ return RoundPath;
+}