Function TestLoopTurningAngle

s2/loop_test.go:1514–1584

(t *testing.T)

}

func TestLoopTurningAngle(t *testing.T) {
	tests := []struct {
		loop *Loop
		want float64
	}{
		{EmptyLoop(), 2 * math.Pi},
		{FullLoop(), -2 * math.Pi},
		{northHemi3, 0},
		{westHemi, 0},
		{candyCane, 4.69364376125922},
		{lineTriangle, 2 * math.Pi},
		{skinnyChevron, 2 * math.Pi},
	}

	for _, test := range tests {
		if got := test.loop.TurningAngle(); !float64Near(got, test.want, epsilon) {
			t.Errorf("%v.TurningAngle() = %v, want %v", test.loop, got, test.want)
		}

		// Check that the turning angle is *identical* when the vertex order is
		// rotated, and that the sign is inverted when the vertices are reversed.
		expected := test.loop.TurningAngle()
		loopCopy := cloneLoop(test.loop)
		for i := 0; i < len(test.loop.vertices); i++ {
			loopCopy.Invert()
			if got := loopCopy.TurningAngle(); got != -expected {
				t.Errorf("loop.Invert().TurningAngle() = %v, want %v", got, -expected)
			}
			// Invert it back to normal.
			loopCopy.Invert()

			loopCopy = rotate(loopCopy)
			if got := loopCopy.TurningAngle(); got != expected {
				t.Errorf("loop.TurningAngle() = %v, want %v", got, expected)
			}
		}
	}

	// Build a narrow spiral loop starting at the north pole. This is designed
	// to test that the error in TurningAngle is linear in the number of
	// vertices even when the partial sum of the turning angles gets very large.
	// The spiral consists of two arms defining opposite sides of the loop.
	const armPoints = 10000 // Number of vertices in each "arm"
	const armRadius = 0.01  // Radius of spiral.
	var vertices = make([]Point, 2*armPoints)

	// Set the center point of the spiral.
	vertices[armPoints] = PointFromCoords(0, 0, 1)

	for i := range armPoints {
		angle := (2 * math.Pi / 3) * float64(i)
		x := math.Cos(angle)
		y := math.Sin(angle)
		r1 := float64(i) * armRadius / armPoints
		r2 := (float64(i) + 1.5) * armRadius / armPoints
		vertices[armPoints-i-1] = PointFromCoords(r1*x, r1*y, 1)
		vertices[armPoints+i] = PointFromCoords(r2*x, r2*y, 1)
	}