491 lines
22 KiB
C#
491 lines
22 KiB
C#
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using System.Collections;
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using System.Collections.Generic;
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using UnityEngine;
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namespace EzySlice {
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/**
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* Contains static functionality to perform geometric intersection tests.
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*/
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public sealed class Intersector {
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/**
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* Perform an intersection between Plane and Line, storing intersection point
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* in reference q. Function returns true if intersection has been found or
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* false otherwise.
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*/
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public static bool Intersect(Plane pl, Line ln, out Vector3 q) {
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return Intersector.Intersect(pl, ln.positionA, ln.positionB, out q);
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}
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public const float Epsilon = 0.0001f;
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/**
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* Perform an intersection between Plane and Line made up of points a and b. Intersection
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* point will be stored in reference q. Function returns true if intersection has been
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* found or false otherwise.
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*/
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public static bool Intersect(Plane pl, Vector3 a, Vector3 b, out Vector3 q) {
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Vector3 normal = pl.normal;
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Vector3 ab = b - a;
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float t = (pl.dist - Vector3.Dot(normal, a)) / Vector3.Dot(normal, ab);
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// need to be careful and compensate for floating errors
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if (t >= -Epsilon && t <= (1 + Epsilon)) {
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q = a + t * ab;
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return true;
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}
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q = Vector3.zero;
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return false;
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}
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/**
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* Support functionality
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*/
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public static float TriArea2D(float x1, float y1, float x2, float y2, float x3, float y3) {
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return (x1 - x2) * (y2 - y3) - (x2 - x3) * (y1 - y2);
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}
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/**
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* Perform an intersection between Plane and Triangle. This is a comprehensive function
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* which alwo builds a HULL Hirearchy useful for decimation projects. This obviously
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* comes at the cost of more complex code and runtime checks, but the returned results
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* are much more flexible.
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* Results will be filled into the IntersectionResult reference. Check result.isValid()
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* for the final results.
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*/
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public static void Intersect(Plane pl, Triangle tri, IntersectionResult result) {
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// clear the previous results from the IntersectionResult
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result.Clear();
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// grab local variables for easier access
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Vector3 a = tri.positionA;
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Vector3 b = tri.positionB;
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Vector3 c = tri.positionC;
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// check to see which side of the plane the points all
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// lay in. SideOf operation is a simple dot product and some comparison
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// operations, so these are a very quick checks
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SideOfPlane sa = pl.SideOf(a);
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SideOfPlane sb = pl.SideOf(b);
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SideOfPlane sc = pl.SideOf(c);
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// we cannot intersect if the triangle points all fall on the same side
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// of the plane. This is an easy early out test as no intersections are possible.
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if (sa == sb && sb == sc) {
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return;
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}
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// detect cases where two points lay straight on the plane, meaning
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// that the plane is actually parralel with one of the edges of the triangle
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else if ((sa == SideOfPlane.ON && sa == sb) ||
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(sa == SideOfPlane.ON && sa == sc) ||
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(sb == SideOfPlane.ON && sb == sc)) {
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return;
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}
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// detect cases where one point is on the plane and the other two are on the same side
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else if ((sa == SideOfPlane.ON && sb != SideOfPlane.ON && sb == sc) ||
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(sb == SideOfPlane.ON && sa != SideOfPlane.ON && sa == sc) ||
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(sc == SideOfPlane.ON && sa != SideOfPlane.ON && sa == sb)) {
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return;
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}
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// keep in mind that intersection points are shared by both
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// the upper HULL and lower HULL hence they lie perfectly
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// on the plane that cut them
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Vector3 qa;
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Vector3 qb;
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// check the cases where the points of the triangle actually lie on the plane itself
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// in these cases, there is only going to be 2 triangles, one for the upper HULL and
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// the other on the lower HULL
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// we just need to figure out which points to accept into the upper or lower hulls.
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if (sa == SideOfPlane.ON) {
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// if the point a is on the plane, test line b-c
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if (Intersector.Intersect(pl, b, c, out qa)) {
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// line b-c intersected, construct out triangles and return approprietly
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result.AddIntersectionPoint(qa);
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result.AddIntersectionPoint(a);
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// our two generated triangles, we need to figure out which
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// triangle goes into the UPPER hull and which goes into the LOWER hull
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Triangle ta = new Triangle(a, b, qa);
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Triangle tb = new Triangle(a, qa, c);
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// generate UV coordinates if there is any
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if (tri.hasUV) {
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// the computed UV coordinate if the intersection point
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Vector2 pq = tri.GenerateUV(qa);
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Vector2 pa = tri.uvA;
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Vector2 pb = tri.uvB;
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Vector2 pc = tri.uvC;
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ta.SetUV(pa, pb, pq);
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tb.SetUV(pa, pq, pc);
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}
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// generate Normal coordinates if there is any
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if (tri.hasNormal) {
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// the computed Normal coordinate if the intersection point
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Vector3 pq = tri.GenerateNormal(qa);
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Vector3 pa = tri.normalA;
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Vector3 pb = tri.normalB;
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Vector3 pc = tri.normalC;
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ta.SetNormal(pa, pb, pq);
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tb.SetNormal(pa, pq, pc);
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}
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// generate Tangent coordinates if there is any
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if (tri.hasTangent) {
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// the computed Tangent coordinate if the intersection point
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Vector4 pq = tri.GenerateTangent(qa);
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Vector4 pa = tri.tangentA;
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Vector4 pb = tri.tangentB;
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Vector4 pc = tri.tangentC;
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ta.SetTangent(pa, pb, pq);
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tb.SetTangent(pa, pq, pc);
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}
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// b point lies on the upside of the plane
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if (sb == SideOfPlane.UP) {
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result.AddUpperHull(ta).AddLowerHull(tb);
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}
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// b point lies on the downside of the plane
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else if (sb == SideOfPlane.DOWN) {
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result.AddUpperHull(tb).AddLowerHull(ta);
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}
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}
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}
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// test the case where the b point lies on the plane itself
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else if (sb == SideOfPlane.ON) {
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// if the point b is on the plane, test line a-c
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if (Intersector.Intersect(pl, a, c, out qa)) {
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// line a-c intersected, construct out triangles and return approprietly
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result.AddIntersectionPoint(qa);
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result.AddIntersectionPoint(b);
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// our two generated triangles, we need to figure out which
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// triangle goes into the UPPER hull and which goes into the LOWER hull
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Triangle ta = new Triangle(a, b, qa);
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Triangle tb = new Triangle(qa, b, c);
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// generate UV coordinates if there is any
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if (tri.hasUV) {
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// the computed UV coordinate if the intersection point
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Vector2 pq = tri.GenerateUV(qa);
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Vector2 pa = tri.uvA;
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Vector2 pb = tri.uvB;
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Vector2 pc = tri.uvC;
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ta.SetUV(pa, pb, pq);
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tb.SetUV(pq, pb, pc);
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}
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// generate Normal coordinates if there is any
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if (tri.hasNormal) {
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// the computed Normal coordinate if the intersection point
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Vector3 pq = tri.GenerateNormal(qa);
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Vector3 pa = tri.normalA;
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Vector3 pb = tri.normalB;
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Vector3 pc = tri.normalC;
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ta.SetNormal(pa, pb, pq);
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tb.SetNormal(pq, pb, pc);
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}
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// generate Tangent coordinates if there is any
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if (tri.hasTangent) {
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// the computed Tangent coordinate if the intersection point
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Vector4 pq = tri.GenerateTangent(qa);
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Vector4 pa = tri.tangentA;
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Vector4 pb = tri.tangentB;
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Vector4 pc = tri.tangentC;
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ta.SetTangent(pa, pb, pq);
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tb.SetTangent(pq, pb, pc);
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}
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// a point lies on the upside of the plane
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if (sa == SideOfPlane.UP) {
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result.AddUpperHull(ta).AddLowerHull(tb);
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}
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// a point lies on the downside of the plane
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else if (sa == SideOfPlane.DOWN) {
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result.AddUpperHull(tb).AddLowerHull(ta);
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}
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}
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}
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// test the case where the c point lies on the plane itself
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else if (sc == SideOfPlane.ON) {
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// if the point c is on the plane, test line a-b
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if (Intersector.Intersect(pl, a, b, out qa)) {
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// line a-c intersected, construct out triangles and return approprietly
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result.AddIntersectionPoint(qa);
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result.AddIntersectionPoint(c);
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// our two generated triangles, we need to figure out which
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// triangle goes into the UPPER hull and which goes into the LOWER hull
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Triangle ta = new Triangle(a, qa, c);
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Triangle tb = new Triangle(qa, b, c);
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// generate UV coordinates if there is any
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if (tri.hasUV) {
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// the computed UV coordinate if the intersection point
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Vector2 pq = tri.GenerateUV(qa);
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Vector2 pa = tri.uvA;
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Vector2 pb = tri.uvB;
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Vector2 pc = tri.uvC;
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ta.SetUV(pa, pq, pc);
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tb.SetUV(pq, pb, pc);
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}
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// generate Normal coordinates if there is any
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if (tri.hasNormal) {
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// the computed Normal coordinate if the intersection point
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Vector3 pq = tri.GenerateNormal(qa);
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Vector3 pa = tri.normalA;
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Vector3 pb = tri.normalB;
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Vector3 pc = tri.normalC;
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ta.SetNormal(pa, pq, pc);
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tb.SetNormal(pq, pb, pc);
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}
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// generate Tangent coordinates if there is any
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if (tri.hasTangent) {
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// the computed Tangent coordinate if the intersection point
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Vector4 pq = tri.GenerateTangent(qa);
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Vector4 pa = tri.tangentA;
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Vector4 pb = tri.tangentB;
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Vector4 pc = tri.tangentC;
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ta.SetTangent(pa, pq, pc);
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tb.SetTangent(pq, pb, pc);
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}
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// a point lies on the upside of the plane
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if (sa == SideOfPlane.UP) {
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result.AddUpperHull(ta).AddLowerHull(tb);
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}
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// a point lies on the downside of the plane
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else if (sa == SideOfPlane.DOWN) {
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result.AddUpperHull(tb).AddLowerHull(ta);
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}
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}
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}
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// at this point, all edge cases have been tested and failed, we need to perform
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// full intersection tests against the lines. From this point onwards we will generate
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// 3 triangles
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else if (sa != sb && Intersector.Intersect(pl, a, b, out qa)) {
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// intersection found against a - b
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result.AddIntersectionPoint(qa);
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// since intersection was found against a - b, we need to check which other
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// lines to check (we only need to check one more line) for intersection.
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// the line we check against will be the line against the point which lies on
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// the other side of the plane.
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if (sa == sc) {
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// we likely have an intersection against line b-c which will complete this loop
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if (Intersector.Intersect(pl, b, c, out qb)) {
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result.AddIntersectionPoint(qb);
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// our three generated triangles. Two of these triangles will end
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// up on either the UPPER or LOWER hulls.
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Triangle ta = new Triangle(qa, b, qb);
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Triangle tb = new Triangle(a, qa, qb);
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Triangle tc = new Triangle(a, qb, c);
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// generate UV coordinates if there is any
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if (tri.hasUV) {
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// the computed UV coordinate if the intersection point
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Vector2 pqa = tri.GenerateUV(qa);
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Vector2 pqb = tri.GenerateUV(qb);
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Vector2 pa = tri.uvA;
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Vector2 pb = tri.uvB;
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Vector2 pc = tri.uvC;
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ta.SetUV(pqa, pb, pqb);
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tb.SetUV(pa, pqa, pqb);
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tc.SetUV(pa, pqb, pc);
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}
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// generate Normal coordinates if there is any
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if (tri.hasNormal) {
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// the computed Normal coordinate if the intersection point
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Vector3 pqa = tri.GenerateNormal(qa);
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Vector3 pqb = tri.GenerateNormal(qb);
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Vector3 pa = tri.normalA;
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Vector3 pb = tri.normalB;
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Vector3 pc = tri.normalC;
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ta.SetNormal(pqa, pb, pqb);
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tb.SetNormal(pa, pqa, pqb);
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tc.SetNormal(pa, pqb, pc);
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}
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// generate Tangent coordinates if there is any
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if (tri.hasTangent) {
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// the computed Tangent coordinate if the intersection point
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Vector4 pqa = tri.GenerateTangent(qa);
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Vector4 pqb = tri.GenerateTangent(qb);
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Vector4 pa = tri.tangentA;
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Vector4 pb = tri.tangentB;
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Vector4 pc = tri.tangentC;
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ta.SetTangent(pqa, pb, pqb);
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tb.SetTangent(pa, pqa, pqb);
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tc.SetTangent(pa, pqb, pc);
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}
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if (sa == SideOfPlane.UP) {
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result.AddUpperHull(tb).AddUpperHull(tc).AddLowerHull(ta);
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} else {
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result.AddLowerHull(tb).AddLowerHull(tc).AddUpperHull(ta);
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}
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}
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} else {
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// in this scenario, the point a is a "lone" point which lies in either upper
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// or lower HULL. We need to perform another intersection to find the last point
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if (Intersector.Intersect(pl, a, c, out qb)) {
|
||
|
|
result.AddIntersectionPoint(qb);
|
||
|
|
|
||
|
|
// our three generated triangles. Two of these triangles will end
|
||
|
|
// up on either the UPPER or LOWER hulls.
|
||
|
|
Triangle ta = new Triangle(a, qa, qb);
|
||
|
|
Triangle tb = new Triangle(qa, b, c);
|
||
|
|
Triangle tc = new Triangle(qb, qa, c);
|
||
|
|
|
||
|
|
// generate UV coordinates if there is any
|
||
|
|
if (tri.hasUV) {
|
||
|
|
// the computed UV coordinate if the intersection point
|
||
|
|
Vector2 pqa = tri.GenerateUV(qa);
|
||
|
|
Vector2 pqb = tri.GenerateUV(qb);
|
||
|
|
Vector2 pa = tri.uvA;
|
||
|
|
Vector2 pb = tri.uvB;
|
||
|
|
Vector2 pc = tri.uvC;
|
||
|
|
|
||
|
|
ta.SetUV(pa, pqa, pqb);
|
||
|
|
tb.SetUV(pqa, pb, pc);
|
||
|
|
tc.SetUV(pqb, pqa, pc);
|
||
|
|
}
|
||
|
|
|
||
|
|
// generate Normal coordinates if there is any
|
||
|
|
if (tri.hasNormal) {
|
||
|
|
// the computed Normal coordinate if the intersection point
|
||
|
|
Vector3 pqa = tri.GenerateNormal(qa);
|
||
|
|
Vector3 pqb = tri.GenerateNormal(qb);
|
||
|
|
Vector3 pa = tri.normalA;
|
||
|
|
Vector3 pb = tri.normalB;
|
||
|
|
Vector3 pc = tri.normalC;
|
||
|
|
|
||
|
|
ta.SetNormal(pa, pqa, pqb);
|
||
|
|
tb.SetNormal(pqa, pb, pc);
|
||
|
|
tc.SetNormal(pqb, pqa, pc);
|
||
|
|
}
|
||
|
|
|
||
|
|
// generate Tangent coordinates if there is any
|
||
|
|
if (tri.hasTangent) {
|
||
|
|
// the computed Tangent coordinate if the intersection point
|
||
|
|
Vector4 pqa = tri.GenerateTangent(qa);
|
||
|
|
Vector4 pqb = tri.GenerateTangent(qb);
|
||
|
|
Vector4 pa = tri.tangentA;
|
||
|
|
Vector4 pb = tri.tangentB;
|
||
|
|
Vector4 pc = tri.tangentC;
|
||
|
|
|
||
|
|
ta.SetTangent(pa, pqa, pqb);
|
||
|
|
tb.SetTangent(pqa, pb, pc);
|
||
|
|
tc.SetTangent(pqb, pqa, pc);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (sa == SideOfPlane.UP) {
|
||
|
|
result.AddUpperHull(ta).AddLowerHull(tb).AddLowerHull(tc);
|
||
|
|
} else {
|
||
|
|
result.AddLowerHull(ta).AddUpperHull(tb).AddUpperHull(tc);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// if line a-b did not intersect (or the lie on the same side of the plane)
|
||
|
|
// this simplifies the problem a fair bit. This means we have an intersection
|
||
|
|
// in line a-c and b-c, which we can use to build a new UPPER and LOWER hulls
|
||
|
|
// we are expecting both of these intersection tests to pass, otherwise something
|
||
|
|
// went wrong (float errors? missed a checked case?)
|
||
|
|
else if (Intersector.Intersect(pl, c, a, out qa) && Intersector.Intersect(pl, c, b, out qb)) {
|
||
|
|
// in here we know that line a-b actually lie on the same side of the plane, this will
|
||
|
|
// simplify the rest of the logic. We also have our intersection points
|
||
|
|
// the computed UV coordinate of the intersection point
|
||
|
|
|
||
|
|
result.AddIntersectionPoint(qa);
|
||
|
|
result.AddIntersectionPoint(qb);
|
||
|
|
|
||
|
|
// our three generated triangles. Two of these triangles will end
|
||
|
|
// up on either the UPPER or LOWER hulls.
|
||
|
|
Triangle ta = new Triangle(qa, qb, c);
|
||
|
|
Triangle tb = new Triangle(a, qb, qa);
|
||
|
|
Triangle tc = new Triangle(a, b, qb);
|
||
|
|
|
||
|
|
// generate UV coordinates if there is any
|
||
|
|
if (tri.hasUV) {
|
||
|
|
// the computed UV coordinate if the intersection point
|
||
|
|
Vector2 pqa = tri.GenerateUV(qa);
|
||
|
|
Vector2 pqb = tri.GenerateUV(qb);
|
||
|
|
Vector2 pa = tri.uvA;
|
||
|
|
Vector2 pb = tri.uvB;
|
||
|
|
Vector2 pc = tri.uvC;
|
||
|
|
|
||
|
|
ta.SetUV(pqa, pqb, pc);
|
||
|
|
tb.SetUV(pa, pqb, pqa);
|
||
|
|
tc.SetUV(pa, pb, pqb);
|
||
|
|
}
|
||
|
|
|
||
|
|
// generate Normal coordinates if there is any
|
||
|
|
if (tri.hasNormal) {
|
||
|
|
// the computed Normal coordinate if the intersection point
|
||
|
|
Vector3 pqa = tri.GenerateNormal(qa);
|
||
|
|
Vector3 pqb = tri.GenerateNormal(qb);
|
||
|
|
Vector3 pa = tri.normalA;
|
||
|
|
Vector3 pb = tri.normalB;
|
||
|
|
Vector3 pc = tri.normalC;
|
||
|
|
|
||
|
|
ta.SetNormal(pqa, pqb, pc);
|
||
|
|
tb.SetNormal(pa, pqb, pqa);
|
||
|
|
tc.SetNormal(pa, pb, pqb);
|
||
|
|
}
|
||
|
|
|
||
|
|
// generate Tangent coordinates if there is any
|
||
|
|
if (tri.hasTangent) {
|
||
|
|
// the computed Tangent coordinate if the intersection point
|
||
|
|
Vector4 pqa = tri.GenerateTangent(qa);
|
||
|
|
Vector4 pqb = tri.GenerateTangent(qb);
|
||
|
|
Vector4 pa = tri.tangentA;
|
||
|
|
Vector4 pb = tri.tangentB;
|
||
|
|
Vector4 pc = tri.tangentC;
|
||
|
|
|
||
|
|
ta.SetTangent(pqa, pqb, pc);
|
||
|
|
tb.SetTangent(pa, pqb, pqa);
|
||
|
|
tc.SetTangent(pa, pb, pqb);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (sa == SideOfPlane.UP) {
|
||
|
|
result.AddUpperHull(tb).AddUpperHull(tc).AddLowerHull(ta);
|
||
|
|
} else {
|
||
|
|
result.AddLowerHull(tb).AddLowerHull(tc).AddUpperHull(ta);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|