#!/usr/bin/env python3 import math import inkex from inkex import Transform, TextElement, Tspan, Color, Circle, PathElement, CubicSuperPath import os import random import numpy as np import openmesh as om import networkx as nx from lxml import etree import copy """ Extension for InkScape 1.0 Paperfold is another flattener for triangle mesh files, heavily based on paperfoldmodels by Felix Scholz aka felixfeliz. Author: Mario Voigt / FabLab Chemnitz Mail: mario.voigt@stadtfabrikanten.org Date: 13.09.2020 Last patch: 10.05.2021 License: GNU GPL v3 To run this you need to install OpenMesh with python pip. The algorithm of paperfoldmodels consists of three steps: - Find a minimum spanning tree of the dual graph of the mesh. - Unfold the dual graph. - Remove self-intersections by adding additional cuts along edges. Reference: The code is mostly based on the algorithm presented in a by Straub and Prautzsch (https://geom.ivd.kit.edu/downloads/proj-paper-models_cut_out_sheets.pdf). Module licenses - paperfoldmodels (https://github.com/felixfeliz/paperfoldmodels) - MIT License possible import file types -> https://www.graphics.rwth-aachen.de/media/openmesh_static/Documentations/OpenMesh-8.0-Documentation/a04096.html todo: - option to render all triangles in a detached way (overlapping lines/independent) + merge coplanar adjacent triangles to polygons - write tab and slot generator (like joinery/polyhedra extension) - fstl preview - fix line: dualGraph.add_edge(face1.idx(), face2.idx(), idx=edge.idx(), weight=edgeweight) # #might fail without throwing any error (silent aborts) ... - option to set fill color per face - add some way to merge coplanar triangles (tri-faces) to polygons and keep those polygons (facets) intact. At the moment facets are getting destroyed. Not good for some papercrafts """ class Paperfold(inkex.EffectExtension): angleRangeCalculated = False #set to true after first calculation iteration (needed globally) minAngle = 0 minAngle = 0 angleRange = 0 def getElementChildren(self, element, elements = None): if elements == None: elements = [] if element.tag != inkex.addNS('g','svg'): elements.append(element) for child in element.getchildren(): self.getElementChildren(child, elements) return elements # Compute the third point of a triangle when two points and all edge lengths are given def getThirdPoint(self, v0, v1, l01, l12, l20): v2rotx = (l01 ** 2 + l20 ** 2 - l12 ** 2) / (2 * l01) val = (l01 + l20 + l12) * (l01 + l20 - l12) * (l01 - l20 + l12) * (-l01 + l20 + l12) v2roty0 = np.sqrt(abs(val)) / (2 * l01) v2roty1 = - v2roty0 theta = np.arctan2(v1[1] - v0[1], v1[0] - v0[0]) v2trans0 = np.array( [v2rotx * np.cos(theta) - v2roty0 * np.sin(theta), v2rotx * np.sin(theta) + v2roty0 * np.cos(theta), 0]) v2trans1 = np.array( [v2rotx * np.cos(theta) - v2roty1 * np.sin(theta), v2rotx * np.sin(theta) + v2roty1 * np.cos(theta), 0]) return [v2trans0 + v0, v2trans1 + v0] # Check if two lines intersect def lineIntersection(self, v1, v2, v3, v4, epsilon): d = (v4[1] - v3[1]) * (v2[0] - v1[0]) - (v4[0] - v3[0]) * (v2[1] - v1[1]) u = (v4[0] - v3[0]) * (v1[1] - v3[1]) - (v4[1] - v3[1]) * (v1[0] - v3[0]) v = (v2[0] - v1[0]) * (v1[1] - v3[1]) - (v2[1] - v1[1]) * (v1[0] - v3[0]) if d < 0: u, v, d = -u, -v, -d return ((0 + epsilon) <= u <= (d - epsilon)) and ((0 + epsilon) <= v <= (d - epsilon)) # Check if a point lies inside a triangle def pointInTriangle(self, A, B, C, P, epsilon): v0 = [C[0] - A[0], C[1] - A[1]] v1 = [B[0] - A[0], B[1] - A[1]] v2 = [P[0] - A[0], P[1] - A[1]] cross = lambda u, v: u[0] * v[1] - u[1] * v[0] u = cross(v2, v0) v = cross(v1, v2) d = cross(v1, v0) if d < 0: u, v, d = -u, -v, -d return u >= (0 + epsilon) and v >= (0 + epsilon) and (u + v) <= (d - epsilon) # Check if two triangles intersect def triangleIntersection(self, t1, t2, epsilon): if self.lineIntersection(t1[0], t1[1], t2[0], t2[1], epsilon): return True if self.lineIntersection(t1[0], t1[1], t2[0], t2[2], epsilon): return True if self.lineIntersection(t1[0], t1[1], t2[1], t2[2], epsilon): return True if self.lineIntersection(t1[0], t1[2], t2[0], t2[1], epsilon): return True if self.lineIntersection(t1[0], t1[2], t2[0], t2[2], epsilon): return True if self.lineIntersection(t1[0], t1[2], t2[1], t2[2], epsilon): return True if self.lineIntersection(t1[1], t1[2], t2[0], t2[1], epsilon): return True if self.lineIntersection(t1[1], t1[2], t2[0], t2[2], epsilon): return True if self.lineIntersection(t1[1], t1[2], t2[1], t2[2], epsilon): return True inTri = True inTri = inTri and self.pointInTriangle(t1[0], t1[1], t1[2], t2[0], epsilon) inTri = inTri and self.pointInTriangle(t1[0], t1[1], t1[2], t2[1], epsilon) inTri = inTri and self.pointInTriangle(t1[0], t1[1], t1[2], t2[2], epsilon) if inTri == True: return True inTri = True inTri = inTri and self.pointInTriangle(t2[0], t2[1], t2[2], t1[0], epsilon) inTri = inTri and self.pointInTriangle(t2[0], t2[1], t2[2], t1[1], epsilon) inTri = inTri and self.pointInTriangle(t2[0], t2[1], t2[2], t1[2], epsilon) if inTri == True: return True return False # Functions for visualisation and output def addVisualisationData(self, mesh, unfoldedMesh, originalHalfedges, unfoldedHalfedges, glueNumber, dihedralAngles): for i in range(3): dihedralAngles[unfoldedMesh.edge_handle(unfoldedHalfedges[i]).idx()] = round(math.degrees(mesh.calc_dihedral_angle(originalHalfedges[i])), self.options.roundingDigits) # Information, which edges belong together glueNumber[unfoldedMesh.edge_handle(unfoldedHalfedges[i]).idx()] = mesh.edge_handle(originalHalfedges[i]).idx() # Function that unwinds a spanning tree def unfoldSpanningTree(self, mesh, spanningTree): try: unfoldedMesh = om.TriMesh() # the unfolded mesh numFaces = mesh.n_faces() sizeTree = spanningTree.number_of_edges() numUnfoldedEdges = 3 * numFaces - sizeTree isFoldingEdge = np.zeros(numUnfoldedEdges, dtype=bool) # Indicates whether an edge is folded or cut glueNumber = np.empty(numUnfoldedEdges, dtype=int) # Saves with which edge is glued together dihedralAngles = np.empty(numUnfoldedEdges, dtype=float) # Valley folding or mountain folding connections = np.empty(numFaces, dtype=int) # Saves which original triangle belongs to the unrolled one numFaces = mesh.n_faces() sizeTree = spanningTree.number_of_edges() numUnfoldedEdges = 3 * numFaces - sizeTree # Select the first triangle as desired startingNode = list(spanningTree.nodes())[0] startingTriangle = mesh.face_handle(startingNode) # We unwind the first triangle # All half edges of the first triangle firstHalfEdge = mesh.halfedge_handle(startingTriangle) secondHalfEdge = mesh.next_halfedge_handle(firstHalfEdge) thirdHalfEdge = mesh.next_halfedge_handle(secondHalfEdge) originalHalfEdges = [firstHalfEdge, secondHalfEdge, thirdHalfEdge] # Calculate the lengths of the edges, this will determine the shape of the triangle (congruence) edgelengths = [mesh.calc_edge_length(firstHalfEdge), mesh.calc_edge_length(secondHalfEdge), mesh.calc_edge_length(thirdHalfEdge)] # The first two points firstUnfoldedPoint = np.array([0, 0, 0]) secondUnfoldedPoint = np.array([edgelengths[0], 0, 0]) # We calculate the third point of the triangle from the first two. There are two possibilities [thirdUnfolded0, thirdUnfolded1] = self.getThirdPoint(firstUnfoldedPoint, secondUnfoldedPoint, edgelengths[0], edgelengths[1], edgelengths[2]) if thirdUnfolded0[1] > 0: thirdUnfoldedPoint = thirdUnfolded0 else: thirdUnfoldePoint = thirdUnfolded1 # Add the new corners to the unwound net firstUnfoldedVertex = unfoldedMesh.add_vertex(secondUnfoldedPoint) secondUnfoldedVertex = unfoldedMesh.add_vertex(thirdUnfoldedPoint) thirdUnfoldedVertex = unfoldedMesh.add_vertex(firstUnfoldedPoint) #firstUnfoldedVertex = unfoldedMesh.add_vertex(firstUnfoldedPoint) #secondUnfoldedVertex = unfoldedMesh.add_vertex(secondUnfoldedPoint) #thirdUnfoldedVertex = unfoldedMesh.add_vertex(thirdUnfoldedPoint) # Create the page unfoldedFace = unfoldedMesh.add_face(firstUnfoldedVertex, secondUnfoldedVertex, thirdUnfoldedVertex) # Memory properties of the surface and edges # The half edges in unrolled mesh firstUnfoldedHalfEdge = unfoldedMesh.opposite_halfedge_handle(unfoldedMesh.halfedge_handle(firstUnfoldedVertex)) secondUnfoldedHalfEdge = unfoldedMesh.next_halfedge_handle(firstUnfoldedHalfEdge) thirdUnfoldedHalfEdge = unfoldedMesh.next_halfedge_handle(secondUnfoldedHalfEdge) unfoldedHalfEdges = [firstUnfoldedHalfEdge, secondUnfoldedHalfEdge, thirdUnfoldedHalfEdge] # Associated triangle in 3D mesh connections[unfoldedFace.idx()] = startingTriangle.idx() # Folding direction and adhesive number self.addVisualisationData(mesh, unfoldedMesh, originalHalfEdges, unfoldedHalfEdges, glueNumber, dihedralAngles) if self.angleRangeCalculated is False: self.minAngle = min(dihedralAngles) self.maxAngle = max(dihedralAngles) #sometimes weird large value are returned, like -34345645435464565453356788761029782 if self.minAngle < -180.0: self.minAngle = -180.0 if self.maxAngle > 180.0: self.maxAngle = 180.0 self.angleRange = self.maxAngle - self.minAngle #self.msg(minAngle) #self.msg(maxAngle) #self.msg(angleRange) self.angleRangeCalculated = True halfEdgeConnections = {firstHalfEdge.idx(): firstUnfoldedHalfEdge.idx(), secondHalfEdge.idx(): secondUnfoldedHalfEdge.idx(), thirdHalfEdge.idx(): thirdUnfoldedHalfEdge.idx()} # We walk through the tree for dualEdge in nx.dfs_edges(spanningTree, source=startingNode): try: foldingEdge = mesh.edge_handle(spanningTree[dualEdge[0]][dualEdge[1]]['idx']) # Find the corresponding half edge in the output triangle foldingHalfEdge = mesh.halfedge_handle(foldingEdge, 0) if not (mesh.face_handle(foldingHalfEdge).idx() == dualEdge[0]): foldingHalfEdge = mesh.halfedge_handle(foldingEdge, 1) # Find the corresponding unwound half edge unfoldedLastHalfEdge = unfoldedMesh.halfedge_handle(halfEdgeConnections[foldingHalfEdge.idx()]) # Find the point in the unrolled triangle that is not on the folding edge oppositeUnfoldedVertex = unfoldedMesh.to_vertex_handle(unfoldedMesh.next_halfedge_handle(unfoldedLastHalfEdge)) # We turn the half edges over to lie in the new triangle foldingHalfEdge = mesh.opposite_halfedge_handle(foldingHalfEdge) unfoldedLastHalfEdge = unfoldedMesh.opposite_halfedge_handle(unfoldedLastHalfEdge) # The two corners of the folding edge unfoldedFromVertex = unfoldedMesh.from_vertex_handle(unfoldedLastHalfEdge) unfoldedToVertex = unfoldedMesh.to_vertex_handle(unfoldedLastHalfEdge) # Calculate the edge lengths in the new triangle secondHalfEdgeInFace = mesh.next_halfedge_handle(foldingHalfEdge) thirdHalfEdgeInFace = mesh.next_halfedge_handle(secondHalfEdgeInFace) originalHalfEdges = [foldingHalfEdge, secondHalfEdgeInFace, thirdHalfEdgeInFace] edgelengths = [mesh.calc_edge_length(foldingHalfEdge), mesh.calc_edge_length(secondHalfEdgeInFace), mesh.calc_edge_length(thirdHalfEdgeInFace)] # We calculate the two possibilities for the third point in the triangle [newUnfoldedVertex0, newUnfoldedVertex1] = self.getThirdPoint(unfoldedMesh.point(unfoldedFromVertex), unfoldedMesh.point(unfoldedToVertex), edgelengths[0], edgelengths[1], edgelengths[2]) newUnfoldedVertex = unfoldedMesh.add_vertex(newUnfoldedVertex0) # Make the face newface = unfoldedMesh.add_face(unfoldedFromVertex, unfoldedToVertex, newUnfoldedVertex) secondUnfoldedHalfEdge = unfoldedMesh.next_halfedge_handle(unfoldedLastHalfEdge) thirdUnfoldedHalfEdge = unfoldedMesh.next_halfedge_handle(secondUnfoldedHalfEdge) unfoldedHalfEdges = [unfoldedLastHalfEdge, secondUnfoldedHalfEdge, thirdUnfoldedHalfEdge] # Saving the information about edges and page # Dotted one's in the output unfoldedLastEdge = unfoldedMesh.edge_handle(unfoldedLastHalfEdge) isFoldingEdge[unfoldedLastEdge.idx()] = True # Gluing number and folding direction self.addVisualisationData(mesh, unfoldedMesh, originalHalfEdges, unfoldedHalfEdges, glueNumber, dihedralAngles) # Related page connections[newface.idx()] = dualEdge[1] # Identify the half edges for i in range(3): halfEdgeConnections[originalHalfEdges[i].idx()] = unfoldedHalfEdges[i].idx() except Exception as e: inkex.utils.debug("Error walking the dual tree at dualEdge {}".format(e)) exit(1) return [unfoldedMesh, isFoldingEdge, connections, glueNumber, dihedralAngles] except Exception as e: inkex.utils.debug("Error: model could not be unfolded. Check for:") inkex.utils.debug(" - watertight model / intact hull") inkex.utils.debug(" - duplicated edges or faces") inkex.utils.debug(" - detached faces or holes") inkex.utils.debug(" - missing units") inkex.utils.debug(" - missing coordinate system") inkex.utils.debug(" - multiple bodies in one file") exit(1) def unfold(self, mesh): # Calculate the number of surfaces, edges and corners, as well as the length of the longest shortest edge numEdges = mesh.n_edges() numVertices = mesh.n_vertices() numFaces = mesh.n_faces() if numFaces > self.options.maxNumFaces: inkex.utils.debug("Aborted. Target STL file has " + str(numFaces) + " faces, but only " + str( self.options.maxNumFaces) + " are allowed.") exit(1) if self.options.printStats is True: inkex.utils.debug("Input STL mesh stats:") inkex.utils.debug("* Number of edges: " + str(numEdges)) inkex.utils.debug("* Number of vertices: " + str(numVertices)) inkex.utils.debug("* Number of faces: " + str(numFaces)) inkex.utils.debug("-----------------------------------------------------------") # Generate the dual graph of the mesh and calculate the weights dualGraph = nx.Graph() # For the weights: calculate the longest and shortest edge of the triangle minLength = 1000 maxLength = 0 for edge in mesh.edges(): edgelength = mesh.calc_edge_length(edge) if edgelength < minLength: minLength = edgelength if edgelength > maxLength: maxLength = edgelength # All edges in the net for edge in mesh.edges(): #inkex.utils.debug("edge.idx = " + str(edge.idx())) # The two sides adjacent to the edge face1 = mesh.face_handle(mesh.halfedge_handle(edge, 0)) face2 = mesh.face_handle(mesh.halfedge_handle(edge, 1)) # The weight edgeweight = 1.0 - (mesh.calc_edge_length(edge) - minLength) / (maxLength - minLength) if self.options.experimentalWeights is True: if round(math.degrees(mesh.calc_dihedral_angle(edge)), self.options.roundingDigits) > 0: edgeweight = 1.0 - (mesh.calc_edge_length(edge) - minLength) / (maxLength - minLength) if round(math.degrees(mesh.calc_dihedral_angle(edge)), self.options.roundingDigits) < 0: edgeweight = -(1.0 - (mesh.calc_edge_length(edge) - minLength) / (maxLength - minLength)) if round(math.degrees(mesh.calc_dihedral_angle(edge)), self.options.roundingDigits) == 0: edgeweight = 0.0 #inkex.utils.debug("edgeweight = " + str(edgeweight)) # Calculate the centres of the pages (only necessary for visualisation) center1 = (0, 0) for vertex in mesh.fv(face1): center1 = center1 + 0.3333333333333333 * np.array([mesh.point(vertex)[0], mesh.point(vertex)[2]]) center2 = (0, 0) for vertex in mesh.fv(face2): center2 = center2 + 0.3333333333333333 * np.array([mesh.point(vertex)[0], mesh.point(vertex)[2]]) # Add the new nodes and edge to the dual graph dualGraph.add_node(face1.idx(), pos=center1) dualGraph.add_node(face2.idx(), pos=center2) dualGraph.add_edge(face1.idx(), face2.idx(), idx=edge.idx(), weight=edgeweight) # #might fail without throwing any error ... # Calculate the minimum spanning tree spanningTree = nx.minimum_spanning_tree(dualGraph) # Unfold the tree fullUnfolding = self.unfoldSpanningTree(mesh, spanningTree) [unfoldedMesh, isFoldingEdge, connections, glueNumber, dihedralAngles] = fullUnfolding # Resolve the intersections # Find all intersections epsilon = 1E-12 # Accuracy faceIntersections = [] for face1 in unfoldedMesh.faces(): for face2 in unfoldedMesh.faces(): if face2.idx() < face1.idx(): # so that we do not double check the couples # Get the triangle faces triangle1 = [] triangle2 = [] for halfedge in unfoldedMesh.fh(face1): triangle1.append(unfoldedMesh.point(unfoldedMesh.from_vertex_handle(halfedge))) for halfedge in unfoldedMesh.fh(face2): triangle2.append(unfoldedMesh.point(unfoldedMesh.from_vertex_handle(halfedge))) if self.triangleIntersection(triangle1, triangle2, epsilon): faceIntersections.append([connections[face1.idx()], connections[face2.idx()]]) # Find the paths # We find the minimum number of cuts to resolve any self-intersection # Search all paths between overlapping triangles paths = [] for intersection in faceIntersections: paths.append( nx.algorithms.shortest_paths.shortest_path(spanningTree, source=intersection[0], target=intersection[1])) # Find all edges in all threads edgepaths = [] for path in paths: edgepath = [] for i in range(len(path) - 1): edgepath.append((path[i], path[i + 1])) edgepaths.append(edgepath) # List of all edges in all paths allEdgesInPaths = list(set().union(*edgepaths)) # Count how often each edge occurs numEdgesInPaths = [] for edge in allEdgesInPaths: num = 0 for path in edgepaths: if edge in path: num = num + 1 numEdgesInPaths.append(num) S = [] C = [] while len(C) != len(paths): # Calculate the weights to decide which edge to cut cutWeights = np.empty(len(allEdgesInPaths)) for i in range(len(allEdgesInPaths)): currentEdge = allEdgesInPaths[i] # Count how many of the paths in which the edge occurs have already been cut numInC = 0 for path in C: if currentEdge in path: numInC = numInC + 1 # Determine the weight if (numEdgesInPaths[i] - numInC) > 0: cutWeights[i] = 1 / (numEdgesInPaths[i] - numInC) else: cutWeights[i] = 1000 # 1000 = infinite # Find the edge with the least weight minimalIndex = np.argmin(cutWeights) S.append(allEdgesInPaths[minimalIndex]) # Find all paths where the edge occurs and add them to C for path in edgepaths: if allEdgesInPaths[minimalIndex] in path and not path in C: C.append(path) # Now we remove the cut edges from the minimum spanning tree spanningTree.remove_edges_from(S) # Find the cohesive components connectedComponents = nx.algorithms.components.connected_components(spanningTree) connectedComponentList = list(connectedComponents) # Unfolding of the components unfoldings = [] for component in connectedComponentList: unfoldings.append(self.unfoldSpanningTree(mesh, spanningTree.subgraph(component))) return fullUnfolding, unfoldings def findBoundingBox(self, mesh): firstpoint = mesh.point(mesh.vertex_handle(0)) xmin = firstpoint[0] xmax = firstpoint[0] ymin = firstpoint[1] ymax = firstpoint[1] for vertex in mesh.vertices(): coordinates = mesh.point(vertex) if (coordinates[0] < xmin): xmin = coordinates[0] if (coordinates[0] > xmax): xmax = coordinates[0] if (coordinates[1] < ymin): ymin = coordinates[1] if (coordinates[1] > ymax): ymax = coordinates[1] boxSize = np.maximum(np.abs(xmax - xmin), np.abs(ymax - ymin)) return [xmin, ymin, boxSize] def writeSVG(self, unfolding, size, randomColorSet): mesh = unfolding[0] isFoldingEdge = unfolding[1] glueNumber = unfolding[3] dihedralAngles = unfolding[4] #statistic values gluePairs = 0 cuts = 0 coplanarEdges = 0 mountainFolds = 0 valleyFolds = 0 # Calculate the bounding box [xmin, ymin, boxSize] = self.findBoundingBox(unfolding[0]) if size > 0: boxSize = size strokewidth = boxSize * self.options.fontSize / 8000 dashLength = boxSize * self.options.fontSize / 2000 spaceLength = boxSize * self.options.fontSize / 800 textDistance = boxSize * self.options.fontSize / 800 textStrokeWidth = boxSize * self.options.fontSize / 3000 fontsize = boxSize * self.options.fontSize / 1000 # Grouping uniqueMainId = self.svg.get_unique_id("") paperfoldPageGroup = self.document.getroot().add(inkex.Group(id=uniqueMainId + "-paperfold-page")) textGroup = inkex.Group(id=uniqueMainId + "-text") edgesGroup = inkex.Group(id=uniqueMainId + "-edges") paperfoldPageGroup.add(textGroup) paperfoldPageGroup.add(edgesGroup) textFacesGroup = inkex.Group(id=uniqueMainId + "-textFaces") textEdgesGroup = inkex.Group(id=uniqueMainId + "-textEdges") textGroup.add(textFacesGroup) textGroup.add(textEdgesGroup) #we could write the unfolded mesh as a 2D stl file to disk if we like: if self.options.writeTwoDSTL is True: if not os.path.exists(self.options.TwoDSTLdir): inkex.utils.debug("Export location for 2D STL unfoldings does not exist. Please select a another dir and try again.") exit(1) else: om.write_mesh(os.path.join(self.options.TwoDSTLdir, uniqueMainId + "-paperfold-page.stl"), mesh) ######################################################### # Nmbering triangle faces with circle around ######################################################### if self.options.printTriangleNumbers is True: for face in mesh.faces(): faceNr = str(face.idx() + 1) centroid = mesh.calc_face_centroid(face) textFaceGroup = inkex.Group(id=uniqueMainId + "-textFace-" + faceNr) circle = textFaceGroup.add(Circle(cx="{:0.6f}".format(centroid[0]), cy="{:0.6f}".format(centroid[1]), r="{:0.6f}".format(fontsize))) circle.set('id', uniqueMainId + "-textFaceCircle-" + faceNr) circle.set("style", "stroke:#000000;stroke-width:{:0.6f}".format(strokewidth/2) + ";fill:none") text = textFaceGroup.add(TextElement(id=uniqueMainId + "-textFaceNumber-" + faceNr)) text.set("x", "{:0.6f}".format(centroid[0])) text.set("y", "{:0.6f}".format(centroid[1] + fontsize / 3)) text.set("font-size", "{:0.6f}".format(fontsize)) text.set("style", "stroke-width {:0.6f}".format(textStrokeWidth) + ";text-anchor:middle;text-align:center") tspan = text.add(Tspan(id=uniqueMainId + "-textFaceNumberTspan-" + faceNr)) tspan.set("x", "{:0.6f}".format(centroid[0])) tspan.set("y", "{:0.6f}".format(centroid[1] + fontsize / 3)) tspan.set("style", "stroke-width {:0.6f}".format(textStrokeWidth) + ";text-anchor:middle;text-align:center") tspan.text = faceNr textFacesGroup.append(textFaceGroup) ######################################################### # Nmbering triangle edges and style them according to their type ######################################################### # Go over all edges of the grid for edge in mesh.edges(): # The two endpoints he = mesh.halfedge_handle(edge, 0) vertex0 = mesh.point(mesh.from_vertex_handle(he)) vertex1 = mesh.point(mesh.to_vertex_handle(he)) # Write a straight line between the two corners line = edgesGroup.add(PathElement()) line.set('d', "M {:0.6f},{:0.6f} {:0.6f},{:0.6f}".format(vertex0[0], vertex0[1], vertex1[0], vertex1[1])) # Colour depending on folding direction lineStyle = {"fill": "none"} lineStyle.update({"stroke": self.options.colorCutEdges}) line.set("id", uniqueMainId + "-cut-edge-" + str(edge.idx())) lineStyle.update({"stroke-width": "{:0.6f}".format(strokewidth)}) lineStyle.update({"stroke-linecap":"butt"}) lineStyle.update({"stroke-linejoin":"miter"}) lineStyle.update({"stroke-miterlimit":"4"}) dihedralAngle = dihedralAngles[edge.idx()] # Dotted lines for folding edges if isFoldingEdge[edge.idx()]: if self.options.dashes is True: lineStyle.update({"stroke-dasharray":"{:0.6f}, {:0.6f}".format(dashLength, spaceLength)}) if dihedralAngle > 0: lineStyle.update({"stroke": self.options.colorMountainFolds}) line.set("id", uniqueMainId + "-mountain-fold-" + str(edge.idx())) mountainFolds += 1 if dihedralAngle < 0: lineStyle.update({"stroke": self.options.colorValleyFolds}) line.set("id", uniqueMainId + "-valley-fold-" + str(edge.idx())) valleyFolds += 1 if dihedralAngle == 0: lineStyle.update({"stroke": self.options.colorCoplanarEdges}) line.set("id", uniqueMainId + "-coplanar-edge-" + str(edge.idx())) if self.options.importCoplanarEdges is False: line.delete() coplanarEdges += 1 else: lineStyle.update({"stroke-dasharray":"none"}) # The number of the edge to be glued if not isFoldingEdge[edge.idx()]: if self.options.separateGluePairsByColor is True: lineStyle.update({"stroke": randomColorSet[glueNumber[edge.idx()]]}) gluePairs += 1 lineStyle.update({"stroke-dashoffset":"0.0"}) lineStyle.update({"stroke-opacity":"1.0"}) if self.options.edgeStyle == "saturationsForAngles": if dihedralAngle != 0: #we dont want to apply HSL adjustments for zero angle lines because they would be invisible then hslColor = inkex.Color(lineStyle.get('stroke')).to_hsl() newSaturation = abs(dihedralAngle / self.angleRange) * 100 #percentage values hslColor.saturation = newSaturation lineStyle.update({"stroke":hslColor.to_rgb()}) elif self.options.edgeStyle == "opacitiesForAngles": if dihedralAngle != 0: #we dont want to apply opacity adjustments for zero angle lines because they would be invisible then opacity = abs(dihedralAngle / 180) lineStyle.update({"stroke-opacity": "{:0.6f}".format(opacity)}) line.style = lineStyle ######################################################### # Textual things ######################################################### halfEdge = mesh.halfedge_handle(edge, 0) # Find halfedge in the face if mesh.face_handle(halfEdge).idx() == -1: halfEdge = mesh.opposite_halfedge_handle(halfEdge) vector = mesh.calc_edge_vector(halfEdge) vector = vector / np.linalg.norm(vector) # normalize midPoint = 0.5 * ( mesh.point(mesh.from_vertex_handle(halfEdge)) + mesh.point(mesh.to_vertex_handle(halfEdge))) rotatedVector = np.array([-vector[1], vector[0], 0]) angle = np.arctan2(vector[1], vector[0]) position = midPoint + textDistance * rotatedVector if self.options.flipLabels is True: position = midPoint - textDistance * rotatedVector rotation = 180 / np.pi * angle if self.options.flipLabels is True: rotation += 180 edgeNr = str(edge.idx() + 1) text = textEdgesGroup.add(TextElement(id=uniqueMainId + "-edgeNumber-" + edgeNr)) text.set("x", "{:0.6f}".format(position[0])) text.set("y", "{:0.6f}".format(position[1])) text.set("font-size", "{:0.6f}".format(fontsize)) text.set("style", "stroke-width {:0.6f}".format(textStrokeWidth) + ";text-anchor:middle;text-align:center") text.set("transform", "rotate({:0.6f} {:0.6f} {:0.6f})".format(rotation, position[0], position[1])) tspan = text.add(Tspan()) tspan.set("x", "{:0.6f}".format(position[0])) tspan.set("y", "{:0.6f}".format(position[1])) tspan.set("style", "stroke-width {:0.6f}".format(textStrokeWidth) + ";text-anchor:middle;text-align:center") tspanText = [] if self.options.printGluePairNumbers is True and not isFoldingEdge[edge.idx()]: tspanText.append(str(glueNumber[edge.idx()] + 1)) if self.options.printAngles is True and dihedralAngle != 0.0: tspanText.append("{:0.2f}°".format(dihedralAngle)) if self.options.printLengths is True: printUnit = True if printUnit is False: unitToPrint = self.svg.unit else: unitToPrint = "" tspanText.append("{:0.2f} {}".format(self.options.scalefactor * math.hypot(vertex1[0] - vertex0[0], vertex1[1] - vertex0[1]), unitToPrint)) tspan.text = " | ".join(tspanText) if tspan.text == "": #if no text we remove again to clean up text.delete() tspan.delete() ''' merge cutting edges to single contour. code ripped off from "join path" extension ''' if self.options.merge_cut_lines is True: cutEdges = [] #find all cutting edges - they have to be sorted to build up a clean continuous line for edge in edgesGroup: edge_id = edge.get('id') if "cut-edge-" in edge_id: cutEdges.append(edge) #find the cutting edge which starts at the previous cutting edge end point paths = {p.get('id'): self.getPartsFromCubicSuper(CubicSuperPath(p.get('d'))) for p in cutEdges } pathIds = [p.get('id') for p in cutEdges] startPathId = pathIds[0] pathIds = self.getArrangedIds(paths, startPathId) newParts = [] firstElem = None for key in pathIds: parts = paths[key] # ~ parts = getPartsFromCubicSuper(cspath) start = parts[0][0][0] elem = self.svg.getElementById(key) if(len(newParts) == 0): newParts += parts[:] firstElem = elem else: if(self.vectCmpWithMargin(start, newParts[-1][-1][-1], margin = .01)): newParts[-1] += parts[0] else: newSeg = [newParts[-1][-1][-1], newParts[-1][-1][-1], start, start] newParts[-1].append(newSeg) newParts[-1] += parts[0] if(len(parts) > 1): newParts += parts[1:] parent = elem.getparent() parent.remove(elem) newElem = copy.copy(firstElem) oldId = firstElem.get('id') newElem.set('d', CubicSuperPath(self.getCubicSuperFromParts(newParts))) newElem.set('id', oldId + '_joined') parent.append(newElem) #insert at the end if len(textFacesGroup) == 0: textFacesGroup.delete() #delete if empty set if len(textEdgesGroup) == 0: textEdgesGroup.delete() #delete if empty set if len(textGroup) == 0: textGroup.delete() #delete if empty set if self.options.printStats is True: inkex.utils.debug(" * Number of cuts: " + str(cuts)) inkex.utils.debug(" * Number of coplanar edges: " + str(coplanarEdges)) inkex.utils.debug(" * Number of mountain folds: " + str(mountainFolds)) inkex.utils.debug(" * Number of valley folds: " + str(valleyFolds)) inkex.utils.debug(" * Number of glue pairs: {:0.0f}".format(gluePairs / 2)) inkex.utils.debug(" * min angle: {:0.2f}".format(self.minAngle)) inkex.utils.debug(" * max angle: {:0.2f}".format(self.maxAngle)) inkex.utils.debug(" * Edge angle range: {:0.2f}".format(self.angleRange)) return paperfoldPageGroup def floatCmpWithMargin(self, float1, float2, margin): return abs(float1 - float2) < margin def vectCmpWithMargin(self, vect1, vect2, margin): return all(self.floatCmpWithMargin(vect2[i], vect1[i], margin) for i in range(0, len(vect1))) def getPartsFromCubicSuper(self, cspath): parts = [] for subpath in cspath: part = [] prevBezPt = None for i, bezierPt in enumerate(subpath): if(prevBezPt != None): seg = [prevBezPt[1], prevBezPt[2], bezierPt[0], bezierPt[1]] part.append(seg) prevBezPt = bezierPt parts.append(part) return parts def getCubicSuperFromParts(self, parts): cbsuper = [] for part in parts: subpath = [] lastPt = None pt = None for seg in part: if(pt == None): ptLeft = seg[0] pt = seg[0] ptRight = seg[1] subpath.append([ptLeft, pt, ptRight]) ptLeft = seg[2] pt = seg[3] subpath.append([ptLeft, pt, pt]) cbsuper.append(subpath) return cbsuper def getArrangedIds(self, pathMap, startPathId): nextPathId = startPathId orderPathIds = [nextPathId] #Arrange in order while(len(orderPathIds) < len(pathMap)): minDist = 9e+100 #A large float closestId = None np = pathMap[nextPathId] npPts = [np[-1][-1][-1]] if(len(orderPathIds) == 1):#compare both the ends for the first path npPts.append(np[0][0][0]) for key in pathMap: if(key in orderPathIds): continue parts = pathMap[key] start = parts[0][0][0] end = parts[-1][-1][-1] for i, npPt in enumerate(npPts): dist = abs(start[0] - npPt[0]) + abs(start[1] - npPt[1]) if(dist < minDist): minDist = dist closestId = key dist = abs(end[0] - npPt[0]) + abs(end[1] - npPt[1]) if(dist < minDist): minDist = dist pathMap[key] = [[[pts for pts in reversed(seg)] for seg in \ reversed(part)] for part in reversed(parts)] closestId = key #If start point of the first path is closer reverse its direction if(i > 0 and closestId == key): pathMap[nextPathId] = [[[pts for pts in reversed(seg)] for seg in \ reversed(part)] for part in reversed(np)] orderPathIds.append(closestId) nextPathId = closestId return orderPathIds def add_arguments(self, pars): pars.add_argument("--tab") #Input pars.add_argument("--inputfile") pars.add_argument("--maxNumFaces", type=int, default=200, help="If the STL file has too much detail it contains a large number of faces. This will make unfolding extremely slow. So we can limit it.") pars.add_argument("--scalefactor", type=float, default=1.0, help="Manual scale factor") pars.add_argument("--roundingDigits", type=int, default=3, help="Digits for rounding") #Output pars.add_argument("--printGluePairNumbers", type=inkex.Boolean, default=False, help="Print glue pair numbers on cut edges") pars.add_argument("--printAngles", type=inkex.Boolean, default=False, help="Print folding angles on edges") pars.add_argument("--printLengths", type=inkex.Boolean, default=False, help="Print lengths on edges") pars.add_argument("--printTriangleNumbers", type=inkex.Boolean, default=False, help="Print triangle numbers on faces") pars.add_argument("--importCoplanarEdges", type=inkex.Boolean, default=False, help="Import coplanar edges") pars.add_argument("--experimentalWeights", type=inkex.Boolean, default=False, help="Mess around with algorithm") pars.add_argument("--printStats", type=inkex.Boolean, default=False, help="Show some unfold statistics") pars.add_argument("--resizetoimport", type=inkex.Boolean, default=True, help="Resize the canvas to the imported drawing's bounding box") pars.add_argument("--extraborder", type=float, default=0.0) pars.add_argument("--extraborderUnits") pars.add_argument("--writeTwoDSTL", type=inkex.Boolean, default=False, help="Write 2D STL unfoldings") pars.add_argument("--TwoDSTLdir", default="./inkscape_export/", help="Location to save exported 2D STL") #Style pars.add_argument("--fontSize", type=int, default=15, help="Label font size (%)") pars.add_argument("--flipLabels", type=inkex.Boolean, default=False, help="Flip labels") pars.add_argument("--dashes", type=inkex.Boolean, default=True, help="Dashes for cut/coplanar edges") pars.add_argument("--merge_cut_lines", type=inkex.Boolean, default=True, help="Merge cut lines") pars.add_argument("--edgeStyle", help="Adjust color saturation or opacity for folding edges. The larger the angle the darker the color") pars.add_argument("--separateGluePairsByColor", type=inkex.Boolean, default=False, help="Separate glue pairs by color") pars.add_argument("--colorCutEdges", type=Color, default='255', help="Cut edges") pars.add_argument("--colorCoplanarEdges", type=Color, default='1943148287', help="Coplanar edges") pars.add_argument("--colorValleyFolds", type=Color, default='3422552319', help="Valley fold edges") pars.add_argument("--colorMountainFolds", type=Color, default='879076607', help="Mountain fold edges") #Post Processing pars.add_argument("--joineryMode", type=inkex.Boolean, default=False, help="Enable joinery mode") pars.add_argument("--origamiSimulatorMode", type=inkex.Boolean, default=False, help="Enable origami simulator mode") def effect(self): if not os.path.exists(self.options.inputfile): inkex.utils.debug("The input file does not exist. Please select a proper file and try again.") exit(1) mesh = om.read_trimesh(self.options.inputfile) #mesh = om.read_polymesh(self.options.inputfile) #we must work with triangles instead of polygons because the algorithm works with that ONLY fullUnfolded, unfoldedComponents = self.unfold(mesh) unfoldComponentCount = len(unfoldedComponents) #if len(unfoldedComponents) == 0: # inkex.utils.debug("Error: no components were unfolded.") # exit(1) if self.options.printStats is True: inkex.utils.debug("Unfolding components: {:0.0f}".format(unfoldComponentCount)) # Compute maxSize of the components # All components must be scaled to the same size as the largest component maxSize = 0 for unfolding in unfoldedComponents: [xmin, ymin, boxSize] = self.findBoundingBox(unfolding[0]) if boxSize > maxSize: maxSize = boxSize xSpacing = maxSize / unfoldComponentCount * 0.1 # 10% spacing between each component; calculated by max box size ######################################################### # mode config for joinery: ######################################################### if self.options.joineryMode is True: self.options.separateGluePairsByColor = True #we need random colors in this mode ######################################################### # mode config for origami simulator: ######################################################### ''' required style for Origami Simulator: colors: - #ff0000 (red) - mountain folds - #0000ff (blue) - valley folds - #000000 (black) - boundary cuts (for both the outline of the pattern and any internal holes) - #ffff00 (yellow) - coplonar triangle edges ("facet creases") (no support for polygons > 3 edges) - #00ff00 (green) - thin slits - #ff00ff (magenta) - undriven creases (swing freely) opacity: - final fold angle of a mountain or valley fold is set by its opacity. Any fold angle between 0° and 180° may be used. For example: - 1.0 = 180° (fully folded) - 0.5 = 90° - 0 = 0° (flat) ''' if self.options.origamiSimulatorMode is True: self.options.joineryMode = True #we set to true even if false because we need the same flat structure for origami simulator self.options.separateGluePairsByColor = False #we need to have no weird random colors in this mode self.options.edgeStyle = "opacitiesForAngles" #highly important for simulation self.options.dashes = False self.options.printGluePairNumbers = False self.options.printAngles = False self.options.printLengths = False self.options.importCoplanarEdges = True self.options.colorCutEdges = "#000000" #black self.options.colorCoplanarEdges = "#ffff00" #yellow self.options.colorMountainFolds = "#ff0000" #red self.options.colorValleyFolds = "#0000ff" #blue #generate random colors; used to identify glue tab pairs randomColorSet = [] if self.options.separateGluePairsByColor: while len(randomColorSet) < len(mesh.edges()): r = lambda: random.randint(0,255) newColor = '#%02X%02X%02X' % (r(),r(),r()) if newColor not in randomColorSet: randomColorSet.append(newColor) # Create a new container group to attach all paperfolds paperfoldMainGroup = self.document.getroot().add(inkex.Group(id=self.svg.get_unique_id("paperfold-"))) #make a new group at root level for i in range(len(unfoldedComponents)): if self.options.printStats is True: inkex.utils.debug("-----------------------------------------------------------") inkex.utils.debug("Unfolding component nr.: {:0.0f}".format(i)) paperfoldPageGroup = self.writeSVG(unfoldedComponents[i], maxSize, randomColorSet) #translate the groups next to each other to remove overlappings if i != 0: #previous_bbox = paperfoldMainGroup[i-1].bounding_box() #as TextElement, Tspan and Circle cause wrong BBox calculation, we have to make it more complex previous_bbox = inkex.BoundingBox() for child in self.getElementChildren(paperfoldMainGroup[i-1]): if not isinstance (child, inkex.TextElement) and \ not isinstance (child, inkex.Tspan) and \ not isinstance (child, inkex.Circle): transform = inkex.Transform() parent = child.getparent() if parent is not None and isinstance(parent, inkex.ShapeElement): transform = parent.composed_transform() previous_bbox += child.bounding_box(transform) #this_bbox = paperfoldPageGroup.bounding_box() this_bbox = inkex.BoundingBox() for child in self.getElementChildren(paperfoldPageGroup): #as TextElement, Tspan and Circle cause wrong BBox calculation, we have to make it more complex if not isinstance (child, inkex.TextElement) and \ not isinstance (child, inkex.Tspan) and \ not isinstance (child, inkex.Circle): transform = inkex.Transform() parent = child.getparent() if parent is not None and isinstance(parent, inkex.ShapeElement): transform = parent.composed_transform() this_bbox += child.bounding_box(transform) #self.msg(previous_bbox) #self.msg(this_bbox) paperfoldPageGroup.set("transform", "translate({:0.6f}, 0.0)".format(previous_bbox.left + previous_bbox.width - this_bbox.left + xSpacing)) paperfoldMainGroup.append(paperfoldPageGroup) #apply scale factor translation_matrix = [[self.options.scalefactor, 0.0, 0.0], [0.0, self.options.scalefactor, 0.0]] paperfoldMainGroup.transform = Transform(translation_matrix) @ paperfoldMainGroup.transform #paperfoldMainGroup.set('transform', 'scale(%f,%f)' % (self.options.scalefactor, self.options.scalefactor)) #adjust canvas to the inserted unfolding if self.options.resizetoimport: bbox = paperfoldMainGroup.bounding_box() namedView = self.document.getroot().find(inkex.addNS('namedview', 'sodipodi')) root = self.svg.getElement('//svg:svg'); offset = self.svg.unittouu(str(self.options.extraborder) + self.options.extraborderUnits) root.set('viewBox', '%f %f %f %f' % (bbox.left - offset, bbox.top - offset, bbox.width + 2 * offset, bbox.height + 2 * offset)) root.set('width', "{:0.6f}{}".format(bbox.width + 2 * offset, self.svg.unit)) root.set('height', "{:0.6f}{}".format(bbox.height + 2 * offset, self.svg.unit)) #if set, we move all edges (path elements) to the top level if self.options.joineryMode is True: for paperfoldPage in paperfoldMainGroup.getchildren(): for child in paperfoldPage: if "-edges" in child.get('id'): for edge in child: edgeTransform = edge.composed_transform() self.document.getroot().append(edge) edge.transform = edgeTransform if __name__ == '__main__': Paperfold().run()