[p5-splines] Always draw splines with a slight curve except for verti…

…cal segments

internal/geom/point.go

@@ -68,3 +68,11 @@ func norm(p P) P {
 	}
 	return p
 }
+
+func rotate(p P, theta float64) P {
+	cs, sn := math.Cos(theta), math.Sin(theta)
+	return P{
+		X: p.X*cs - p.Y*sn,
+		Y: p.X*sn + p.Y*cs, // invert sin e cos to rotate in the SVG plane
+	}
+}

internal/geom/spline_make.go

@@ -0,0 +1,43 @@
+package geom
+
+import "math"
+
+// MakeSpline computes control points of a cubic bezier from a to b so that it gently curves in the
+// direction of the slope.
+func MakeSpline(a, b P) ctrlp {
+	// slide factor
+	const k = 0.2
+	// if the points are vertically aligned, let the cubic degenerate into a straight segment
+	if a.X == b.X {
+		return ctrlp{a, a, b, b}
+	}
+	// compute vector
+	v := P{b.X - a.X, b.Y - a.Y}
+
+	// rotation angle
+	// rotate clockwise when the x of the vector is positive, counterclockwise when is negative
+	// x is inverted to account for rotation in the SVG plane
+	theta1 := sign(-v.X) * math.Pi * (1.0 / 10.0)
+	theta2 := sign(-v.X) * math.Pi * (9.0 / 10.0)
+
+	// rotate the vector
+	r := rotate(v, theta1)
+	q := rotate(v, theta2)
+	// slide the control points along the rotated vector
+	p1 := P{a.X + k*r.X, a.Y + k*r.Y}
+	p2 := P{b.X + k*q.X, b.Y + k*q.Y}
+
+	return ctrlp{
+		p0: a,
+		p1: p1,
+		p2: p2,
+		p3: b,
+	}
+}
+
+func sign(x float64) float64 {
+	if x < 0 {
+		return -1
+	}
+	return 1
+}

internal/phase5/splines.go

@@ -10,9 +10,7 @@ import (
 
 func execSplines(g *graph.DGraph, routes []routableEdge) {
 	for _, e := range routes {
-		if e.From.ID == "a" && e.To.ID == "m" {
-			imonitor.Log("spline", e)
-		}
+		imonitor.Log("spline", e)
 
 		rects := buildRects(g, e)
 
@@ -30,6 +28,16 @@ func execSplines(g *graph.DGraph, routes []routableEdge) {
 		}
 
 		path := geom.Shortest(start, end, rects)
+		// remember the order of the elements in the path slice is from end to start
+
+		// with only two points the path is a straight line
+		// in this case we can skip spline fitting because it would result in a straight segment
+		// instead apply a heuristic to slide the control points just a little
+		// to draw the edge as a gentle curve
+		if len(path) == 2 {
+			e.Points = geom.MakeSpline(start, end).Float64Slice()
+			continue
+		}
 
 		poly := geom.MergeRects(rects)
 		ctrls := geom.FitSpline(path, geom.P{}, geom.P{}, poly.Sides())