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StraightSkeletonGenerator.cs
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StraightSkeletonGenerator.cs
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using System;
using System.Collections.Generic;
using UnityEngine;
namespace ProceduralToolkit.Skeleton
{
/// <summary>
/// A straight skeleton generator, computes a straight skeleton for the input polygon, reusable.
/// The generation algorithm is loosely based on the work of Tom Kelly
/// (2014) "Unwritten procedural modeling with the straight skeleton"
/// http://www.twak.co.uk/2014/02/unwritten-procedural-modeling-with.html
/// </summary>
public class StraightSkeletonGenerator
{
private readonly List<Plan> activePlans = new List<Plan>();
private readonly List<Plan> newPlans = new List<Plan>();
private StraightSkeleton skeleton;
public StraightSkeleton Generate(IList<Vector2> polygon)
{
activePlans.Clear();
newPlans.Clear();
var activePlan = new Plan(polygon);
activePlans.Add(activePlan);
skeleton = new StraightSkeleton(activePlan);
foreach (var p in activePlans)
{
foreach (var vertex in p)
{
CalculateBisector(vertex);
}
}
int count = 0;
while (activePlans.Count > 0)
{
if (count > polygon.Count)
{
Debug.LogError("Too many iterations");
break;
}
bool success = OffsetAndDetectEvents();
if (!success)
{
return skeleton;
}
count++;
}
return skeleton;
}
public List<Plan> GetActivePlans()
{
return activePlans;
}
private bool OffsetAndDetectEvents()
{
ResetInEventFlags();
foreach (var plan in activePlans)
{
float offset = FindSmallestOffset(plan);
if (float.IsPositiveInfinity(offset) || offset <= 0)
{
Debug.LogError("Unable to find offset");
return false;
}
plan.Offset(-offset);
var intersectionEvents = FindIntersectionEvents(plan);
foreach (var intersectionEvent in intersectionEvents)
{
ProcessIntersectionEvent(plan, intersectionEvent);
}
newPlans.AddRange(plan.Split());
}
activePlans.AddRange(newPlans);
newPlans.Clear();
CleanupLoops();
activePlans.RemoveAll(p => p.Count == 0);
skeleton.ValidatePolygons();
return true;
}
private void ResetInEventFlags()
{
foreach (var plan in activePlans)
{
foreach (var vertex in plan)
{
vertex.inEvent = false;
}
}
}
private float FindSmallestOffset(Plan plan)
{
float smallestOffset = float.PositiveInfinity;
foreach (var vertex in plan)
{
float offset;
if (BisectorBisector(vertex, vertex.next, out offset))
{
smallestOffset = Mathf.Min(smallestOffset, offset);
}
if (vertex.reflect)
{
foreach (var segmentA in plan)
{
var segmentB = segmentA.next;
if (segmentA == vertex || segmentB == vertex)
{
continue;
}
if (BisectorSegment(vertex, segmentA.position, segmentB.position, out offset))
{
smallestOffset = Mathf.Min(smallestOffset, offset);
}
}
}
}
return smallestOffset;
}
private List<IntersectionEvent> FindIntersectionEvents(Plan plan)
{
var intersectionEvents = new List<IntersectionEvent>();
var vertex = plan.First;
do
{
CreateSplitVertices(plan, vertex);
var intersectionEvent = FindIntersectionEvent(vertex);
if (intersectionEvent != null)
{
intersectionEvents.Add(intersectionEvent);
if (intersectionEvent.chains[0].Count == plan.Count)
{
return intersectionEvents;
}
}
vertex = vertex.next;
} while (vertex != plan.First);
CompressEvents(intersectionEvents);
return intersectionEvents;
}
private void CreateSplitVertices(Plan plan, Plan.Vertex searchVertex)
{
var vertex = searchVertex;
do
{
if (vertex != searchVertex &&
vertex.next != searchVertex &&
PointSegment(searchVertex.position, vertex.position, vertex.next.position))
{
var newVertex = CreateSplitVertex(plan, searchVertex.position, vertex, vertex.next);
vertex = newVertex.next;
}
else
{
vertex = vertex.next;
}
} while (vertex != searchVertex);
}
private Plan.Vertex CreateSplitVertex(Plan plan, Vector2 position, Plan.Vertex segmentA, Plan.Vertex segmentB)
{
var newVertex = new Plan.Vertex(position)
{
previousPolygonIndex = segmentA.nextPolygonIndex,
nextPolygonIndex = segmentB.previousPolygonIndex
};
plan.Insert(newVertex, segmentA, segmentB);
CalculateBisector(newVertex);
return newVertex;
}
private IntersectionEvent FindIntersectionEvent(Plan.Vertex searchVertex)
{
var vertex = searchVertex;
do
{
if (!vertex.inEvent && vertex != searchVertex && IncidentalVertices(searchVertex, vertex))
{
var intersectionEvent = new IntersectionEvent(searchVertex.position);
ExpandEvent(intersectionEvent, searchVertex);
return intersectionEvent;
}
vertex = vertex.next;
} while (vertex != searchVertex);
return null;
}
private void ExpandEvent(IntersectionEvent intersectionEvent, Plan.Vertex startVertex)
{
var vertex = startVertex;
do
{
if (!vertex.inEvent && IncidentalVertices(intersectionEvent.position, vertex.position))
{
var chain = FindCollapsedChain(vertex);
intersectionEvent.chains.Add(chain);
vertex = chain[chain.Count - 1].next;
}
else
{
vertex = vertex.next;
}
} while (vertex != startVertex);
}
private List<Plan.Vertex> FindCollapsedChain(Plan.Vertex startVertex)
{
startVertex.inEvent = true;
var chain = new List<Plan.Vertex> {startVertex};
var vertex = startVertex;
do
{
if (!vertex.next.inEvent && IncidentalVertices(vertex, vertex.next))
{
vertex.next.inEvent = true;
chain.Add(vertex.next);
vertex = vertex.next;
}
else
{
break;
}
} while (vertex != startVertex);
return chain;
}
private void CompressEvents(List<IntersectionEvent> intersectionEvents)
{
foreach (var intersectionEvent in intersectionEvents)
{
var firstChain = intersectionEvent.chains[0];
var lastChain = intersectionEvent.chains[intersectionEvent.chains.Count - 1];
var lastVertex = lastChain[lastChain.Count - 1];
if (lastVertex.next == firstChain[0])
{
lastChain.AddRange(firstChain);
intersectionEvent.chains[0] = lastChain;
firstChain.Clear();
intersectionEvent.chains.RemoveAt(intersectionEvent.chains.Count - 1);
}
}
}
private void ProcessIntersectionEvent(Plan plan, IntersectionEvent intersectionEvent)
{
foreach (var chain in intersectionEvent.chains)
{
SimplifyChain(plan, chain);
}
intersectionEvent.chains.RemoveAll(c => c.Count == 0);
if (intersectionEvent.chains.Count >= 2)
{
for (var i = 0; i < intersectionEvent.chains.Count; i++)
{
var chain = intersectionEvent.chains[i];
var previousChain = intersectionEvent.chains.GetLooped(i - 1);
var vertex = chain[0];
plan.Remove(vertex);
skeleton.AddVertex(vertex);
var newVertex = new Plan.Vertex(intersectionEvent.position)
{
previousPolygonIndex = vertex.previousPolygonIndex,
nextPolygonIndex = previousChain[0].nextPolygonIndex
};
plan.Insert(newVertex, vertex.previous, previousChain[0].next);
CalculateBisector(newVertex);
}
}
}
private void SimplifyChain(Plan plan, List<Plan.Vertex> chain)
{
if (chain.Count == 1) return;
var first = chain[0];
var previous = first.previous;
var last = chain[chain.Count - 1];
var next = last.next;
foreach (var vertex in chain)
{
plan.Remove(vertex);
skeleton.AddVertex(vertex);
}
chain.Clear();
if (next != first)
{
var newVertex = new Plan.Vertex(first.position)
{
previousPolygonIndex = first.previousPolygonIndex,
nextPolygonIndex = last.nextPolygonIndex,
};
plan.Insert(newVertex, previous, next);
chain.Add(newVertex);
CalculateBisector(newVertex);
}
}
private void CleanupLoops()
{
foreach (var plan in activePlans)
{
if (plan.Count == 1)
{
Debug.LogError("Invalid plan: " + plan.First);
}
else if (plan.Count == 2)
{
var vertex = plan.First;
plan.Remove(vertex);
plan.Remove(vertex.next);
}
}
}
private static void CalculateBisector(Plan.Vertex vertex)
{
Plan.Vertex previous = vertex.previous;
Plan.Vertex next = vertex.next;
float angle;
Vector2 direction = Geometry.GetAngleBisector(previous.position, vertex.position, next.position, out angle);
vertex.angle = angle;
vertex.bisector = direction;
}
private static bool PointSegment(Vector2 point, Vector2 segmentA, Vector2 segmentB)
{
if (!IncidentalVertices(point, segmentA) &&
!IncidentalVertices(point, segmentB))
{
return Intersect.PointSegment(point, segmentA, segmentB);
}
return false;
}
private static bool BisectorBisector(Plan.Vertex vertexA, Plan.Vertex vertexB, out float offset)
{
IntersectionRayRay2 intersection;
if (Intersect.RayRay(vertexA.position, vertexA.bisector, vertexB.position, vertexB.bisector, out intersection))
{
if (intersection.type == IntersectionType.Point)
{
float offsetA = GetBisectorBisectorOffset(vertexA, intersection.pointA);
float offsetB = GetBisectorBisectorOffset(vertexB, intersection.pointA);
offset = Mathf.Min(offsetA, offsetB);
return true;
}
if (intersection.type == IntersectionType.Segment)
{
float toIntersection = Vector2.Distance(vertexA.position, vertexB.position);
float offsetA = GetBisectorBisectorOffset(vertexA, toIntersection)/2;
float offsetB = GetBisectorBisectorOffset(vertexB, toIntersection)/2;
offset = Mathf.Min(offsetA, offsetB);
return true;
}
Debug.LogErrorFormat("Invalid bisector intersection\ntype: {0}\npointA: {1} pointB: {2}\nbisectorA: {3} bisectorB:{4}",
intersection.type, intersection.pointA, intersection.pointB, vertexA.bisector, vertexB.bisector);
offset = 0;
return false;
}
offset = 0;
return false;
}
private static float GetBisectorBisectorOffset(Plan.Vertex vertex, Vector2 intersection)
{
float toIntersection = Vector2.Distance(vertex.position, intersection);
return GetBisectorBisectorOffset(vertex, toIntersection);
}
private static float GetBisectorBisectorOffset(Plan.Vertex vertex, float toIntersection)
{
return toIntersection*Geometry.GetAngleBisectorSin(vertex.angle);
}
private static bool BisectorSegment(Plan.Vertex vertex, Vector2 segmentA, Vector2 segmentB, out float offset)
{
IntersectionRaySegment2 intersection;
if (Intersect.RaySegment(vertex.position, vertex.bisector, segmentA, segmentB, out intersection))
{
if (intersection.type == IntersectionType.Point)
{
Vector2 segmentDirection = (segmentB - segmentA).normalized;
float toIntersection = Vector2.Distance(vertex.position, intersection.pointA);
float intersectionAngle = Vector2.Angle(vertex.bisector, segmentDirection);
float intersectionSin = Mathf.Sin(intersectionAngle*Mathf.Deg2Rad);
float bisectorSin = Geometry.GetAngleBisectorSin(vertex.angle);
offset = toIntersection/(1/intersectionSin + 1/bisectorSin);
return true;
}
Debug.LogErrorFormat("Invalid bisector intersection\ntype: {0}\npointA: {1} pointB: {2}\nray: {3} segmentA:{4} segmentB:{5}",
intersection.type, intersection.pointA, intersection.pointB, vertex.bisector, segmentA, segmentB);
offset = 0;
return false;
}
offset = 0;
return false;
}
private static bool IncidentalVertices(Plan.Vertex a, Plan.Vertex b)
{
return IncidentalVertices(a.position, b.position);
}
private static bool IncidentalVertices(Vector2 a, Vector2 b)
{
return (a - b).sqrMagnitude < Geometry.Epsilon;
}
private class IntersectionEvent
{
public readonly Vector2 position;
public readonly List<List<Plan.Vertex>> chains = new List<List<Plan.Vertex>>();
public IntersectionEvent(Vector2 position)
{
this.position = position;
}
public override string ToString()
{
return String.Format("{0} Count: {1}", position, chains.Count);
}
}
}
}