@threepipe/plugin-svg-renderer/src/three-svg-renderer/core/viewmap/operations/find3dSingularities.ts

Plugins for SVG Rendering of 3d objects for Threepipe

/*
 * Author: Axel Antoine
 * mail: ax.antoine@gmail.com
 * website: http://axantoine.com
 * Created on Tue Nov 22 2022
 *
 * Loki, Inria project-team with Université de Lille
 * within the Joint Research Unit UMR 9189
 * CNRS - Centrale Lille - Université de Lille, CRIStAL
 * https://loki.lille.inria.fr
 *
 * Licence: Licence.md
 */

import {PerspectiveCamera} from "three";
import {Vertex} from "../../../../three-mesh-halfedge";
import {sameSide} from "../../../utils";
import {ViewEdgeNature} from "../ViewEdge";
import {Viewmap} from "../Viewmap";
import {ViewVertex, ViewVertexSingularity} from "../ViewVertex";

export function find3dSingularities(viewmap: Viewmap) {

  const {viewVertexMap, camera} = viewmap;

  for (const [, viewVertex] of viewVertexMap) {
    viewVertex.singularity = singularityForPoint(viewVertex, camera);
  }
}

/**
 *
 * @ref https://hal.inria.fr/hal-02189483/file/contour_tutorial.pdf Section 4.3
 *
 * @param point
 * @param camera
 * @returns
 */
export function singularityForPoint(
    viewVertex: ViewVertex, camera: PerspectiveCamera) {

  const natures = new Set<ViewEdgeNature>();

  let concaveSilhouetteEdgeFound = false;
  let convexSilhouetteEdgeFound = false;

  // Count the number of different natures connected to the vertex
  for (const edge of viewVertex.viewEdges) {

    natures.add(edge.nature);

    if (edge.faces.length > 1 && edge.nature === ViewEdgeNature.Silhouette) {
      concaveSilhouetteEdgeFound ||= edge.isConcave;
      convexSilhouetteEdgeFound ||= !edge.isConcave;
    }
  }

  if (natures.size === 0) {
    console.error("No natures found around vertex", viewVertex);
    return ViewVertexSingularity.None;
  }

  // If the number of segment natures is 1 and there is more than 2 segments
  // connected to the point, then there is a bifurcation singularity
  if (natures.size === 1) {
    if(viewVertex.viewEdges.length > 2 && (
      natures.has(ViewEdgeNature.Silhouette) || natures.has(ViewEdgeNature.Boundary)
    )) {
      return ViewVertexSingularity.Bifurcation;
    }
  }

  // If there are at least 2 edges of different natures connected to the vertex,
  // then there is a mesh intersection singularity
  if (natures.size > 1) {
    if (natures.has(ViewEdgeNature.Silhouette) ||
        natures.has(ViewEdgeNature.Boundary) ||
        natures.has(ViewEdgeNature.MeshIntersection)) {
      return ViewVertexSingularity.MeshIntersection;
    }
  }

  // Curtains folds:

  // Curtain fold singularity can occur on a non-boundary segment where
  // there are at least one concave and one convex edges connected
  // if (!natures.has(EdgeNature.Boundary) &&
  if (concaveSilhouetteEdgeFound && convexSilhouetteEdgeFound) {
    return ViewVertexSingularity.CurtainFold;
  }

  // Curtain fold singularity can also occur on a Boundary edge where
  // one of the connected face overlaps the boundary edge
  // Note that at this stage of the pipeline, each point should only have
  // one associated vertex, hence the index 0
  if (natures.has(ViewEdgeNature.Boundary)) {
    if (isAnyFaceOverlappingBoundary(viewVertex, camera)) {
      return ViewVertexSingularity.CurtainFold;
    }
  }

  return ViewVertexSingularity.None;

}

export function *listBoundaryHalfedgesInOut(vertex: Vertex) {
  yield* vertex.boundaryHalfedgesInLoop();
  yield* vertex.boundaryHalfedgesOutLoop();
}

/**
 * Checks if face adjacent to a boundary vertex overlap in image-space.
 *
 * @ref https://hal.inria.fr/hal-02189483/file/contour_tutorial.pdf Appendix C.2.1
 *
 * @param vertex
 * @param camera
 * @returns
 */
export function isAnyFaceOverlappingBoundary(viewVertex: ViewVertex, camera: PerspectiveCamera) {

  for (const vertex of viewVertex.vertices) {

    // Get the farthest boundary halfedge from the camera and connected to the
    // vertex
    let farthestHalfedge = null;
    let otherVertex = null;
    let distance = -Infinity;

    for (const halfedge of listBoundaryHalfedgesInOut(vertex)) {

      let other;
      if (halfedge.vertex === vertex) {
        // Halfedge is starting from vertex
        other = halfedge.next.vertex;
      } else {
        // Halfedge is arriving to vertex
        other = halfedge.vertex;
      }
      const d = other.position.distanceTo(camera.position);
      if (d > distance) {
        distance = d;
        farthestHalfedge = halfedge;
        otherVertex = other;
      }
    }

    if (farthestHalfedge && otherVertex) {

      // Iterate on each connected faces to vertex and check if it overlaps
      // the farthest halfedge
      const c = camera.position;
      const p = vertex.position;
      const e = otherVertex.position;

      const boundaryFace = farthestHalfedge.twin.face;

      if (boundaryFace) {
        for (const halfedge of vertex.loopCW()) {
          if (halfedge.face !== boundaryFace) {

            const q = halfedge.next.vertex.position;
            const r = halfedge.next.vertex.position;

            if (!sameSide(p,q,r,c,e) && sameSide(c,p,q,e,r) && sameSide(c,p,r,e,q)) {
              return true;
            }
          }
        }
      } else {
        console.error("Boundary halfedge twin has no connected face");
      }
    }
  }
  return false;
}