refactor SDF interface to completely use gonum types

form2/must2/basic.go

@@ -31,7 +31,7 @@ func (s *circle) Evaluate(p r2.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box of a 2d circle.
-func (s *circle) BoundingBox() r2.Box {
+func (s *circle) Bounds() r2.Box {
 	return s.bb
 }
 
@@ -60,7 +60,7 @@ func (s *box) Evaluate(p r2.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box for a 2d box.
-func (s *box) BoundingBox() r2.Box {
+func (s *box) Bounds() r2.Box {
 	return s.bb
 }
 
@@ -92,6 +92,6 @@ func (s *line) Evaluate(p r2.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box for a 2d line.
-func (s *line) BoundingBox() r2.Box {
+func (s *line) Bounds() r2.Box {
 	return s.bb
 }

form2/must2/poly.go

@@ -107,7 +107,7 @@ func (s *polygon) Evaluate(p r2.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box of a 2d polygon.
-func (s *polygon) BoundingBox() r2.Box {
+func (s *polygon) Bounds() r2.Box {
 	return s.bb
 }
 

form3/basic.go

@@ -80,8 +80,8 @@ func Cone(height, r0, r1, round float64) (s sdf.SDF3, err error) {
 // ChamferedCylinder intersects a chamfered cylinder with an SDF3.
 func ChamferedCylinder(s sdf.SDF3, kb, kt float64) (sdf.SDF3, error) {
 	// get the length and radius from the bounding box
-	l := s.BoundingBox().Max.Z
-	r := s.BoundingBox().Max.X
+	l := s.Bounds().Max.Z
+	r := s.Bounds().Max.X
 	p := form2.NewPolygon()
 	p.Add(0, -l)
 	p.Add(r, -l).Chamfer(r * kb)

form3/must3/cylinders.go

@@ -41,7 +41,7 @@ func (s *box) Evaluate(p r3.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box for a 3d box.
-func (s *box) BoundingBox() r3.Box {
+func (s *box) Bounds() r3.Box {
 	return s.bb
 }
 
@@ -72,7 +72,7 @@ func (s *sphere) Evaluate(p r3.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box for a sphere.
-func (s *sphere) BoundingBox() r3.Box {
+func (s *sphere) Bounds() r3.Box {
 	return s.bb
 }
 
@@ -121,7 +121,7 @@ func (s *cylinder) Evaluate(p r3.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box for a cylinder.
-func (s *cylinder) BoundingBox() r3.Box {
+func (s *cylinder) Bounds() r3.Box {
 	return s.bb
 }
 
@@ -201,7 +201,7 @@ func (s *cone) Evaluate(p r3.Vec) float64 {
 }
 
 // BoundingBox return the bounding box for the trucated cone..
-func (s *cone) BoundingBox() r3.Box {
+func (s *cone) Bounds() r3.Box {
 	return s.bb
 }
 
@@ -234,8 +234,8 @@ func sdfBox3d(p, s r3.Vec) float64 {
 // ChamferedCylinder intersects a chamfered cylinder with an SDF3.
 func ChamferedCylinder(s sdf.SDF3, kb, kt float64) sdf.SDF3 {
 	// get the length and radius from the bounding box
-	l := s.BoundingBox().Max.Z
-	r := s.BoundingBox().Max.X
+	l := s.Bounds().Max.Z
+	r := s.Bounds().Max.X
 	p := form2.NewPolygon()
 	p.Add(0, -l)
 	p.Add(r, -l).Chamfer(r * kb)

form3/must3/screw.go

@@ -79,6 +79,6 @@ func (s *screw) Evaluate(p r3.Vec) float64 {
 }
 
 // BoundingBox returns the bounding box for a 3d screw form.
-func (s *screw) BoundingBox() r3.Box {
+func (s *screw) Bounds() r3.Box {
 	return s.bb
 }

matrix.go

@@ -510,3 +510,47 @@ func (a m22) Inverse() m22 {
 	m.x11 = a.x00 * d
 	return m
 }
+
+// rotateToVector returns the rotation matrix that transforms a onto the same direction as b.
+func rotateToVec(a, b r3.Vec) m44 {
+	// is either vector == 0?
+	if d3.EqualWithin(a, r3.Vec{}, epsilon) || d3.EqualWithin(b, r3.Vec{}, epsilon) {
+		return Identity3d()
+	}
+	// normalize both vectors
+	a = r3.Unit(a)
+	b = r3.Unit(b)
+	// are the vectors the same?
+	if d3.EqualWithin(a, b, epsilon) {
+		return Identity3d()
+	}
+
+	// are the vectors opposite (180 degrees apart)?
+	if d3.EqualWithin(r3.Scale(-1, a), b, epsilon) {
+		return m44{
+			-1, 0, 0, 0,
+			0, -1, 0, 0,
+			0, 0, -1, 0,
+			0, 0, 0, 1,
+		}
+	}
+	// general case
+	// See:	https://math.stackexchange.com/questions/180418/calculate-rotation-matrix-to-align-vector-a-to-vector-b-in-3d
+	v := r3.Cross(a, b)
+	vx := r3.Skew(v)
+
+	k := 1 / (1 + r3.Dot(a, b))
+	vx2 := r3.NewMat(nil)
+	vx2.Mul(vx, vx)
+	vx2.Scale(k, vx2)
+
+	// Calculate sum of matrices.
+	vx.Add(vx, r3.Eye())
+	vx.Add(vx, vx2)
+	return m44{
+		vx.At(0, 0), vx.At(0, 1), vx.At(0, 2), 0,
+		vx.At(1, 0), vx.At(1, 1), vx.At(1, 2), 0,
+		vx.At(2, 0), vx.At(2, 1), vx.At(2, 2), 0,
+		0, 0, 0, 1,
+	}
+}

render/internal_test.go

@@ -35,7 +35,7 @@ func TestSTLWriteReadback(t *testing.T) {
 		TotalLength: 40.,
 		ShankLength: 10.0,
 	})
-	size := r3.Norm(d3.Box(s0.BoundingBox()).Size())
+	size := r3.Norm(d3.Box(s0.Bounds()).Size())
 	// calculate relative tolerance
 	rtol := tol * size / quality
 	input, err := RenderAll(NewOctreeRenderer(s0, quality))

render/kdrender.go

@@ -72,7 +72,7 @@ func (s kdSDF) Nearest(v r3.Vec) kdTriangle {
 	return got.(kdTriangle)
 }
 
-func (s kdSDF) BoundingBox() r3.Box {
+func (s kdSDF) Bounds() r3.Box {
 	bb := s.tree.Root.Bounding
 	if bb == nil {
 		panic("got nil bounding box?")

render/kdrender_test.go

@@ -29,7 +29,7 @@ func TestKDSDF(t *testing.T) {
 	}
 	t.Error(len(model), "triangles")
 	kdf := render.NewKDSDF(model)
-	t.Error(kdf.BoundingBox())
+	t.Error(kdf.Bounds())
 	start := time.Now()
 	outside := kdf.Evaluate(r3.Vec{2, 0, 0}) // evaluate point outside bounds
 	inside := kdf.Evaluate(r3.Vec{0, 0, 0})  // evaluate point inside bounds

render/octree_renderer.go

@@ -35,7 +35,7 @@ func NewOctreeRenderer(s sdf.SDF3, meshCells int) *octree {
 	}
 	// Scale the bounding box about the center to make sure the boundaries
 	// aren't on the object surface.
-	bb := d3.Box(s.BoundingBox())
+	bb := d3.Box(s.Bounds())
 	bb = bb.ScaleAboutCenter(1.01)
 	longAxis := d3.Max(bb.Size())
 	// We want to test the smallest cube (side == resolution) for emptiness