Former/mesh_unwrap.go

package main

import (
	"fmt"
	"math"
	"strings"
)

type meshVertex struct{ X, Y, Z float64 }
type meshTri struct{ V [3]int }
type meshEdge struct{ V0, V1 int } // canonical: V0 < V1
type flatVert struct{ X, Y float64 }

type flatTri struct {
	V      [3]flatVert
	TriIdx int
}

type meshUnwrapResult struct {
	Triangles []flatTri
	FoldEdges [][2]flatVert
	CutEdges  [][2]flatVert
	BoundsW   float64
	BoundsH   float64
}

func canonEdge(a, b int) meshEdge {
	if a > b {
		a, b = b, a
	}
	return meshEdge{a, b}
}

// indexMesh merges coincident vertices and returns an indexed representation.
func indexMesh(triangles [][3]Point) ([]meshVertex, []meshTri) {
	const eps = 1e-6
	const gridSize = 1e-5

	type gridKey struct{ ix, iy, iz int64 }
	buckets := make(map[gridKey][]int)
	var verts []meshVertex

	quantize := func(v float64) int64 {
		return int64(math.Floor(v / gridSize))
	}

	findOrAdd := func(x, y, z float64) int {
		gk := gridKey{quantize(x), quantize(y), quantize(z)}
		// Check 27 neighboring cells
		for dx := int64(-1); dx <= 1; dx++ {
			for dy := int64(-1); dy <= 1; dy++ {
				for dz := int64(-1); dz <= 1; dz++ {
					nk := gridKey{gk.ix + dx, gk.iy + dy, gk.iz + dz}
					for _, idx := range buckets[nk] {
						v := verts[idx]
						d := (v.X-x)*(v.X-x) + (v.Y-y)*(v.Y-y) + (v.Z-z)*(v.Z-z)
						if d < eps*eps {
							return idx
						}
					}
				}
			}
		}
		idx := len(verts)
		verts = append(verts, meshVertex{x, y, z})
		buckets[gk] = append(buckets[gk], idx)
		return idx
	}

	rawVerts := len(triangles) * 3
	tris := make([]meshTri, len(triangles))
	for i, t := range triangles {
		tris[i].V[0] = findOrAdd(t[0].X, t[0].Y, t[0].Z)
		tris[i].V[1] = findOrAdd(t[1].X, t[1].Y, t[1].Z)
		tris[i].V[2] = findOrAdd(t[2].X, t[2].Y, t[2].Z)
	}

	debugLog("  indexMesh: %d raw vertices -> %d merged, %d triangles", rawVerts, len(verts), len(tris))
	return verts, tris
}

// buildAdjacency maps each edge to the triangle indices that share it.
func buildAdjacency(tris []meshTri) map[meshEdge][]int {
	adj := make(map[meshEdge][]int)
	for i, t := range tris {
		for e := 0; e < 3; e++ {
			edge := canonEdge(t.V[e], t.V[(e+1)%3])
			adj[edge] = append(adj[edge], i)
		}
	}

	manifold, boundary := 0, 0
	for _, v := range adj {
		if len(v) == 2 {
			manifold++
		} else if len(v) == 1 {
			boundary++
		}
	}
	debugLog("  buildAdjacency: %d edges, %d manifold, %d boundary", len(adj), manifold, boundary)
	return adj
}

func dist3D(verts []meshVertex, a, b int) float64 {
	dx := verts[b].X - verts[a].X
	dy := verts[b].Y - verts[a].Y
	dz := verts[b].Z - verts[a].Z
	return math.Sqrt(dx*dx + dy*dy + dz*dz)
}

func triArea2D(a, b, c flatVert) float64 {
	return 0.5 * ((b.X-a.X)*(c.Y-a.Y) - (c.X-a.X)*(b.Y-a.Y))
}

// placeThirdVertex positions a point given two known 2D points and
// the 3D distances from each to the unknown point.
// side: +1 or -1 to select which side of the edge.
func placeThirdVertex(p0, p1 flatVert, d0, d1 float64, side float64) flatVert {
	dx := p1.X - p0.X
	dy := p1.Y - p0.Y
	d := math.Sqrt(dx*dx + dy*dy)
	if d < 1e-12 {
		return p0
	}
	a := (d0*d0 - d1*d1 + d*d) / (2 * d)
	hSq := d0*d0 - a*a
	if hSq < 0 {
		hSq = 0
	}
	h := math.Sqrt(hSq)
	mx := p0.X + a*dx/d
	my := p0.Y + a*dy/d
	return flatVert{
		X: mx + side*h*dy/d,
		Y: my - side*h*dx/d,
	}
}

// unfoldMesh performs BFS tree-based greedy unfolding of a triangle mesh.
func unfoldMesh(verts []meshVertex, tris []meshTri, adj map[meshEdge][]int) *meshUnwrapResult {
	n := len(tris)
	if n == 0 {
		return &meshUnwrapResult{}
	}

	debugLog("  unfoldMesh: %d triangles, %d vertices", n, len(verts))

	placed := make([]bool, n)
	flat := make([]flatTri, n)

	// Track which edges are in the spanning tree
	treeEdges := make(map[meshEdge]bool)

	type bfsItem struct {
		triIdx    int
		parentIdx int
		sharedE   meshEdge
	}

	var result meshUnwrapResult
	islandOffsetX := 0.0
	islandCount := 0

	for seed := 0; seed < n; seed++ {
		if placed[seed] {
			continue
		}
		islandCount++

		// Place the seed triangle
		t := tris[seed]
		d01 := dist3D(verts, t.V[0], t.V[1])
		d02 := dist3D(verts, t.V[0], t.V[2])
		d12 := dist3D(verts, t.V[1], t.V[2])

		// Skip degenerate triangles
		if d01 < 1e-12 || d02 < 1e-12 || d12 < 1e-12 {
			debugLog("    degenerate seed triangle %d, skipping", seed)
			placed[seed] = true
			continue
		}

		flat[seed].TriIdx = seed
		flat[seed].V[0] = flatVert{islandOffsetX, 0}
		flat[seed].V[1] = flatVert{islandOffsetX + d01, 0}
		flat[seed].V[2] = placeThirdVertex(flat[seed].V[0], flat[seed].V[1], d02, d12, 1)
		placed[seed] = true

		queue := []bfsItem{}

		// Enqueue neighbors of seed
		for e := 0; e < 3; e++ {
			edge := canonEdge(t.V[e], t.V[(e+1)%3])
			for _, nb := range adj[edge] {
				if nb != seed && !placed[nb] {
					queue = append(queue, bfsItem{nb, seed, edge})
				}
			}
		}

		for len(queue) > 0 {
			item := queue[0]
			queue = queue[1:]

			if placed[item.triIdx] {
				continue
			}

			ct := tris[item.triIdx]

			// Find the shared edge vertex indices in the child triangle
			sharedA, sharedB := item.sharedE.V0, item.sharedE.V1
			childThirdVert := -1
			for _, vi := range ct.V {
				if vi != sharedA && vi != sharedB {
					childThirdVert = vi
					break
				}
			}
			if childThirdVert < 0 {
				continue
			}

			// Find 2D positions of shared edge from parent
			pt := tris[item.parentIdx]
			pf := flat[item.parentIdx]
			var p2dA, p2dB flatVert
			var parentThird flatVert
			for vi := 0; vi < 3; vi++ {
				if pt.V[vi] == sharedA {
					p2dA = pf.V[vi]
				}
				if pt.V[vi] == sharedB {
					p2dB = pf.V[vi]
				}
				if pt.V[vi] != sharedA && pt.V[vi] != sharedB {
					parentThird = pf.V[vi]
				}
			}

			// Determine which side of the edge the parent's third vertex is on
			cross := (p2dB.X-p2dA.X)*(parentThird.Y-p2dA.Y) - (p2dB.Y-p2dA.Y)*(parentThird.X-p2dA.X)
			side := -1.0
			if cross < 0 {
				side = 1.0
			}

			dCA := dist3D(verts, childThirdVert, sharedA)
			dCB := dist3D(verts, childThirdVert, sharedB)
			if dCA < 1e-12 || dCB < 1e-12 {
				placed[item.triIdx] = true
				continue
			}

			newVert := placeThirdVertex(p2dA, p2dB, dCA, dCB, side)

			// Assign 2D positions to child triangle vertices
			flat[item.triIdx].TriIdx = item.triIdx
			for vi := 0; vi < 3; vi++ {
				if ct.V[vi] == sharedA {
					flat[item.triIdx].V[vi] = p2dA
				} else if ct.V[vi] == sharedB {
					flat[item.triIdx].V[vi] = p2dB
				} else {
					flat[item.triIdx].V[vi] = newVert
				}
			}
			placed[item.triIdx] = true
			treeEdges[item.sharedE] = true

			// Enqueue neighbors
			for e := 0; e < 3; e++ {
				edge := canonEdge(ct.V[e], ct.V[(e+1)%3])
				for _, nb := range adj[edge] {
					if !placed[nb] {
						queue = append(queue, bfsItem{nb, item.triIdx, edge})
					}
				}
			}
		}

		// Compute island bounds for offset
		minX, maxX := math.Inf(1), math.Inf(-1)
		for i := 0; i < n; i++ {
			if !placed[i] {
				continue
			}
			for _, v := range flat[i].V {
				if v.X < minX {
					minX = v.X
				}
				if v.X > maxX {
					maxX = v.X
				}
			}
		}
		if maxX > islandOffsetX {
			islandOffsetX = maxX + 10.0
		}
	}

	debugLog("  unfoldMesh: %d islands", islandCount)

	// Collect placed triangles and classify edges
	minX, minY := math.Inf(1), math.Inf(1)
	maxX, maxY := math.Inf(-1), math.Inf(-1)

	for i := 0; i < n; i++ {
		if flat[i].V[0] == (flatVert{}) && flat[i].V[1] == (flatVert{}) && flat[i].V[2] == (flatVert{}) {
			// Unplaced degenerate triangle
			continue
		}
		result.Triangles = append(result.Triangles, flat[i])
		for _, v := range flat[i].V {
			if v.X < minX {
				minX = v.X
			}
			if v.X > maxX {
				maxX = v.X
			}
			if v.Y < minY {
				minY = v.Y
			}
			if v.Y > maxY {
				maxY = v.Y
			}
		}
	}

	// Classify edges
	for edge, triList := range adj {
		if len(triList) < 1 {
			continue
		}

		// Find 2D positions for this edge from first triangle that has it placed
		var eA, eB flatVert
		found := false
		for _, ti := range triList {
			t := tris[ti]
			f := flat[ti]
			for vi := 0; vi < 3; vi++ {
				ni := (vi + 1) % 3
				if canonEdge(t.V[vi], t.V[ni]) == edge {
					eA = f.V[vi]
					eB = f.V[ni]
					found = true
					break
				}
			}
			if found {
				break
			}
		}
		if !found {
			continue
		}

		if len(triList) == 1 || !treeEdges[edge] {
			result.CutEdges = append(result.CutEdges, [2]flatVert{eA, eB})
		} else if treeEdges[edge] {
			result.FoldEdges = append(result.FoldEdges, [2]flatVert{eA, eB})
		}
	}

	// Translate to positive quadrant with margin
	margin := 5.0
	offsetX := margin - minX
	offsetY := margin - minY
	for i := range result.Triangles {
		for vi := range result.Triangles[i].V {
			result.Triangles[i].V[vi].X += offsetX
			result.Triangles[i].V[vi].Y += offsetY
		}
	}
	for i := range result.FoldEdges {
		for vi := range result.FoldEdges[i] {
			result.FoldEdges[i][vi].X += offsetX
			result.FoldEdges[i][vi].Y += offsetY
		}
	}
	for i := range result.CutEdges {
		for vi := range result.CutEdges[i] {
			result.CutEdges[i][vi].X += offsetX
			result.CutEdges[i][vi].Y += offsetY
		}
	}

	result.BoundsW = (maxX - minX) + 2*margin
	result.BoundsH = (maxY - minY) + 2*margin
	debugLog("  unfoldMesh: %d placed triangles, %d fold edges, %d cut edges, bounds %.1f x %.1f mm",
		len(result.Triangles), len(result.FoldEdges), len(result.CutEdges), result.BoundsW, result.BoundsH)

	return &result
}

// GenerateMeshUnwrapSVG produces an SVG string from the unfolded mesh.
func GenerateMeshUnwrapSVG(result *meshUnwrapResult) string {
	var b strings.Builder

	w := result.BoundsW
	h := result.BoundsH
	if w < 1 {
		w = 100
	}
	if h < 1 {
		h = 100
	}

	b.WriteString(fmt.Sprintf(`<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 %.2f %.2f" width="%.2fmm" height="%.2fmm">`, w, h, w, h))
	b.WriteString("\n<style>\n")
	b.WriteString("  .panel { fill: none; stroke: #333; stroke-width: 0.3; }\n")
	b.WriteString("  .fold-line { stroke: #aaa; stroke-width: 0.15; stroke-dasharray: 2,1; }\n")
	b.WriteString("  .cut-line { stroke: #333; stroke-width: 0.4; }\n")
	b.WriteString("</style>\n")

	// White background for printing
	b.WriteString(fmt.Sprintf(`<rect width="%.2f" height="%.2f" fill="white"/>`, w, h))
	b.WriteString("\n")

	// Triangles
	for _, t := range result.Triangles {
		b.WriteString(fmt.Sprintf(`<polygon class="panel" points="%.4f,%.4f %.4f,%.4f %.4f,%.4f"/>`,
			t.V[0].X, t.V[0].Y, t.V[1].X, t.V[1].Y, t.V[2].X, t.V[2].Y))
		b.WriteString("\n")
	}

	// Fold edges
	for _, e := range result.FoldEdges {
		b.WriteString(fmt.Sprintf(`<line class="fold-line" x1="%.4f" y1="%.4f" x2="%.4f" y2="%.4f"/>`,
			e[0].X, e[0].Y, e[1].X, e[1].Y))
		b.WriteString("\n")
	}

	// Cut edges
	for _, e := range result.CutEdges {
		b.WriteString(fmt.Sprintf(`<line class="cut-line" x1="%.4f" y1="%.4f" x2="%.4f" y2="%.4f"/>`,
			e[0].X, e[0].Y, e[1].X, e[1].Y))
		b.WriteString("\n")
	}

	b.WriteString("</svg>\n")

	debugLog("GenerateMeshUnwrapSVG: %d triangles, %d fold, %d cut edges, %.0f x %.0f mm",
		len(result.Triangles), len(result.FoldEdges), len(result.CutEdges), w, h)

	return b.String()
}