agent-tools/mesh-tool/mesh/primitives.go

package mesh

import "math"

// All primitives are centered at the origin with +Y up and get outward
// (counter-clockwise) winding; ensureOutward fixes the global
// orientation via the signed volume as a safety net.

func ensureOutward(m *Mesh) *Mesh {
	if m.SignedVolume() < 0 {
		m.FlipWinding()
	}
	return m
}

// Box builds an axis-aligned box of the given size.
func Box(size Vec3) *Mesh {
	x, y, z := size.X/2, size.Y/2, size.Z/2
	m := &Mesh{
		Name: "box",
		Verts: []Vec3{
			{-x, -y, -z}, {x, -y, -z}, {x, y, -z}, {-x, y, -z}, // back  (z-)
			{-x, -y, z}, {x, -y, z}, {x, y, z}, {-x, y, z}, // front (z+)
		},
	}
	quads := [][4]int{
		{0, 3, 2, 1}, // back
		{4, 5, 6, 7}, // front
		{0, 1, 5, 4}, // bottom
		{2, 3, 7, 6}, // top
		{1, 2, 6, 5}, // right
		{0, 4, 7, 3}, // left
	}
	for _, q := range quads {
		m.Tris = append(m.Tris, Triangle{q[0], q[1], q[2]}, Triangle{q[0], q[2], q[3]})
	}
	return ensureOutward(m)
}

// Plane builds a flat rectangle in the XZ plane (an open mesh).
func Plane(w, d float64) *Mesh {
	x, z := w/2, d/2
	return &Mesh{
		Name:  "plane",
		Verts: []Vec3{{-x, 0, -z}, {x, 0, -z}, {x, 0, z}, {-x, 0, z}},
		Tris:  []Triangle{{0, 2, 1}, {0, 3, 2}}, // +Y facing
	}
}

// Sphere builds a UV sphere. segments = around the equator (>= 3),
// rings = from pole to pole (>= 2).
func Sphere(r float64, segments, rings int) *Mesh {
	if segments < 3 {
		segments = 3
	}
	if rings < 2 {
		rings = 2
	}
	m := &Mesh{Name: "sphere"}
	top := len(m.Verts)
	m.Verts = append(m.Verts, Vec3{0, r, 0})
	// interior rings, top to bottom
	ringStart := make([]int, rings)
	for i := 1; i < rings; i++ {
		theta := math.Pi * float64(i) / float64(rings)
		y := r * math.Cos(theta)
		rad := r * math.Sin(theta)
		ringStart[i] = len(m.Verts)
		for j := 0; j < segments; j++ {
			phi := 2 * math.Pi * float64(j) / float64(segments)
			m.Verts = append(m.Verts, Vec3{rad * math.Cos(phi), y, rad * math.Sin(phi)})
		}
	}
	bottom := len(m.Verts)
	m.Verts = append(m.Verts, Vec3{0, -r, 0})

	at := func(ring, seg int) int { return ringStart[ring] + seg%segments }
	for j := 0; j < segments; j++ {
		m.Tris = append(m.Tris, Triangle{top, at(1, j), at(1, j+1)}) // top cap
		m.Tris = append(m.Tris, Triangle{bottom, at(rings-1, j+1), at(rings-1, j)})
	}
	for i := 1; i < rings-1; i++ {
		for j := 0; j < segments; j++ {
			a, b := at(i, j), at(i, j+1)
			c, d := at(i+1, j+1), at(i+1, j)
			m.Tris = append(m.Tris, Triangle{a, b, c}, Triangle{a, c, d})
		}
	}
	return ensureOutward(m)
}

// Cylinder builds a closed cylinder of height h around the Y axis.
func Cylinder(r, h float64, segments int) *Mesh {
	if segments < 3 {
		segments = 3
	}
	m := &Mesh{Name: "cylinder"}
	y := h / 2
	topC := len(m.Verts)
	m.Verts = append(m.Verts, Vec3{0, y, 0})
	botC := len(m.Verts)
	m.Verts = append(m.Verts, Vec3{0, -y, 0})
	topStart := len(m.Verts)
	for j := 0; j < segments; j++ {
		phi := 2 * math.Pi * float64(j) / float64(segments)
		m.Verts = append(m.Verts, Vec3{r * math.Cos(phi), y, r * math.Sin(phi)})
	}
	botStart := len(m.Verts)
	for j := 0; j < segments; j++ {
		phi := 2 * math.Pi * float64(j) / float64(segments)
		m.Verts = append(m.Verts, Vec3{r * math.Cos(phi), -y, r * math.Sin(phi)})
	}
	t := func(j int) int { return topStart + j%segments }
	b := func(j int) int { return botStart + j%segments }
	for j := 0; j < segments; j++ {
		m.Tris = append(m.Tris,
			Triangle{topC, t(j + 1), t(j)},     // top cap
			Triangle{botC, b(j), b(j + 1)},     // bottom cap
			Triangle{t(j), t(j + 1), b(j + 1)}, // side
			Triangle{t(j), b(j + 1), b(j)},     // side
		)
	}
	return ensureOutward(m)
}

// Cone builds a closed cone with its base at -h/2 and apex at +h/2.
func Cone(r, h float64, segments int) *Mesh {
	if segments < 3 {
		segments = 3
	}
	m := &Mesh{Name: "cone"}
	apex := len(m.Verts)
	m.Verts = append(m.Verts, Vec3{0, h / 2, 0})
	baseC := len(m.Verts)
	m.Verts = append(m.Verts, Vec3{0, -h / 2, 0})
	start := len(m.Verts)
	for j := 0; j < segments; j++ {
		phi := 2 * math.Pi * float64(j) / float64(segments)
		m.Verts = append(m.Verts, Vec3{r * math.Cos(phi), -h / 2, r * math.Sin(phi)})
	}
	at := func(j int) int { return start + j%segments }
	for j := 0; j < segments; j++ {
		m.Tris = append(m.Tris,
			Triangle{apex, at(j + 1), at(j)},
			Triangle{baseC, at(j), at(j + 1)},
		)
	}
	return ensureOutward(m)
}

// Torus builds a torus around the Y axis: ring radius R (center of tube
// to center of torus) and tube radius r.
func Torus(R, r float64, segments, rings int) *Mesh {
	if segments < 3 {
		segments = 3
	}
	if rings < 3 {
		rings = 3
	}
	m := &Mesh{Name: "torus"}
	for i := 0; i < segments; i++ { // around the main ring
		phi := 2 * math.Pi * float64(i) / float64(segments)
		cx, cz := math.Cos(phi), math.Sin(phi)
		for j := 0; j < rings; j++ { // around the tube
			theta := 2 * math.Pi * float64(j) / float64(rings)
			rad := R + r*math.Cos(theta)
			m.Verts = append(m.Verts, Vec3{rad * cx, r * math.Sin(theta), rad * cz})
		}
	}
	at := func(i, j int) int { return (i%segments)*rings + j%rings }
	for i := 0; i < segments; i++ {
		for j := 0; j < rings; j++ {
			a, b := at(i, j), at(i+1, j)
			c, d := at(i+1, j+1), at(i, j+1)
			m.Tris = append(m.Tris, Triangle{a, b, c}, Triangle{a, c, d})
		}
	}
	return ensureOutward(m)
}