/**
* Calculate the Barycentric coordinate weight values u-v-w for Point p in respect to the provided
* triangle. This is useful for computing new UV coordinates for arbitrary points.
*/
public Vector3 Barycentric(Vector3 p)
{
Vector3 a = m_pos_a;
Vector3 b = m_pos_b;
Vector3 c = m_pos_c;
Vector3 m = Vector3.Cross(b - a, c - a);
float nu;
float nv;
float ood;
float x = Mathf.Abs(m.x);
float y = Mathf.Abs(m.y);
float z = Mathf.Abs(m.z);
// compute areas of plane with largest projections
if (x >= y && x >= z)
{
// area of PBC in yz plane
nu = Intersector.TriArea2D(p.y, p.z, b.y, b.z, c.y, c.z);
// area of PCA in yz plane
nv = Intersector.TriArea2D(p.y, p.z, c.y, c.z, a.y, a.z);
// 1/2*area of ABC in yz plane
ood = 1.0f / m.x;
}
else if (y >= x && y >= z)
{
// project in xz plane
nu = Intersector.TriArea2D(p.x, p.z, b.x, b.z, c.x, c.z);
nv = Intersector.TriArea2D(p.x, p.z, c.x, c.z, a.x, a.z);
ood = 1.0f / -m.y;
}
else
{
// project in xy plane
nu = Intersector.TriArea2D(p.x, p.y, b.x, b.y, c.x, c.y);
nv = Intersector.TriArea2D(p.x, p.y, c.x, c.y, a.x, a.y);
ood = 1.0f / m.z;
}
float u = nu * ood;
float v = nv * ood;
float w = 1.0f - u - v;
return(new Vector3(u, v, w));
}
/**
* O(n log n) Convex Hull Algorithm.
* Accepts a list of vertices as Vector3 and triangulates them according to a projection
* plane defined as planeNormal. Algorithm will output vertices, indices and UV coordinates
* as arrays
*/
public static bool MonotoneChain(List <Vector3> vertices, Vector3 normal, out List <Triangle> tri, TextureRegion texRegion)
{
int count = vertices.Count;
// we cannot triangulate less than 3 points. Use minimum of 3 points
if (count < 3)
{
tri = null;
return(false);
}
// first, we map from 3D points into a 2D plane represented by the provided normal
Vector3 u = Vector3.Normalize(Vector3.Cross(normal, Vector3.up));
if (Vector3.zero == u)
{
u = Vector3.Normalize(Vector3.Cross(normal, Vector3.forward));
}
Vector3 v = Vector3.Cross(u, normal);
// generate an array of mapped values
Mapped2D[] mapped = new Mapped2D[count];
// these values will be used to generate new UV coordinates later on
float maxDivX = float.MinValue;
float maxDivY = float.MinValue;
float minDivX = float.MaxValue;
float minDivY = float.MaxValue;
// map the 3D vertices into the 2D mapped values
for (int i = 0; i < count; i++)
{
Vector3 vertToAdd = vertices[i];
Mapped2D newMappedValue = new Mapped2D(vertToAdd, u, v);
Vector2 mapVal = newMappedValue.mappedValue;
// grab our maximal values so we can map UV's in a proper range
maxDivX = Mathf.Max(maxDivX, mapVal.x);
maxDivY = Mathf.Max(maxDivY, mapVal.y);
minDivX = Mathf.Min(minDivX, mapVal.x);
minDivY = Mathf.Min(minDivY, mapVal.y);
mapped[i] = newMappedValue;
}
// sort our newly generated array values
Array.Sort <Mapped2D>(mapped, (a, b) => {
Vector2 x = a.mappedValue;
Vector2 p = b.mappedValue;
return((x.x < p.x || (x.x == p.x && x.y < p.y)) ? -1 : 1);
});
// our final hull mappings will end up in here
Mapped2D[] hulls = new Mapped2D[count + 1];
int k = 0;
// build the lower hull of the chain
for (int i = 0; i < count; i++)
{
while (k >= 2)
{
Vector2 mA = hulls[k - 2].mappedValue;
Vector2 mB = hulls[k - 1].mappedValue;
Vector2 mC = mapped[i].mappedValue;
if (Intersector.TriArea2D(mA.x, mA.y, mB.x, mB.y, mC.x, mC.y) > 0.0f)
{
break;
}
k--;
}
hulls[k++] = mapped[i];
}
// build the upper hull of the chain
for (int i = count - 2, t = k + 1; i >= 0; i--)
{
while (k >= t)
{
Vector2 mA = hulls[k - 2].mappedValue;
Vector2 mB = hulls[k - 1].mappedValue;
Vector2 mC = mapped[i].mappedValue;
if (Intersector.TriArea2D(mA.x, mA.y, mB.x, mB.y, mC.x, mC.y) > 0.0f)
{
break;
}
k--;
}
hulls[k++] = mapped[i];
}
// finally we can build our mesh, generate all the variables
// and fill them up
int vertCount = k - 1;
int triCount = (vertCount - 2) * 3;
// this should not happen, but here just in case
if (vertCount < 3)
{
tri = null;
return(false);
}
// ensure List does not dynamically grow, performing copy ops each time!
tri = new List <Triangle>(triCount / 3);
float width = maxDivX - minDivX;
float height = maxDivY - minDivY;
int indexCount = 1;
// generate both the vertices and uv's in this loop
for (int i = 0; i < triCount; i += 3)
{
// the Vertices in our triangle
Mapped2D posA = hulls[0];
Mapped2D posB = hulls[indexCount];
Mapped2D posC = hulls[indexCount + 1];
// generate UV Maps
Vector2 uvA = posA.mappedValue;
Vector2 uvB = posB.mappedValue;
Vector2 uvC = posC.mappedValue;
uvA.x = (uvA.x - minDivX) / width;
uvA.y = (uvA.y - minDivY) / height;
uvB.x = (uvB.x - minDivX) / width;
uvB.y = (uvB.y - minDivY) / height;
uvC.x = (uvC.x - minDivX) / width;
uvC.y = (uvC.y - minDivY) / height;
Triangle newTriangle = new Triangle(posA.originalValue, posB.originalValue, posC.originalValue);
// ensure our UV coordinates are mapped into the requested TextureRegion
newTriangle.SetUV(texRegion.Map(uvA), texRegion.Map(uvB), texRegion.Map(uvC));
// the normals is the same for all vertices since the final mesh is completly flat
newTriangle.SetNormal(normal, normal, normal);
newTriangle.ComputeTangents();
tri.Add(newTriangle);
indexCount++;
}
return(true);
}
/**
* Perform an intersection between Plane and Triangle. This is a comprehensive function
* which alwo builds a HULL Hirearchy useful for decimation projects. This obviously
* comes at the cost of more complex code and runtime checks, but the returned results
* are much more flexible.
* Results will be filled into the IntersectionResult reference. Check result.isValid()
* for the final results.
*/
public static void Intersect(Plane pl, Triangle tri, IntersectionResult result)
{
// clear the previous results from the IntersectionResult
result.Clear();
// grab local variables for easier access
Vector3 a = tri.positionA;
Vector3 b = tri.positionB;
Vector3 c = tri.positionC;
// check to see which side of the plane the points all
// lay in. SideOf operation is a simple dot product and some comparison
// operations, so these are a very quick checks
SideOfPlane sa = pl.SideOf(a);
SideOfPlane sb = pl.SideOf(b);
SideOfPlane sc = pl.SideOf(c);
// we cannot intersect if the triangle points all fall on the same side
// of the plane. This is an easy early out test as no intersections are possible.
if (sa == sb && sb == sc)
{
return;
}
// detect cases where two points lay straight on the plane, meaning
// that the plane is actually parralel with one of the edges of the triangle
else if ((sa == SideOfPlane.ON && sa == sb) ||
(sa == SideOfPlane.ON && sa == sc) ||
(sb == SideOfPlane.ON && sb == sc))
{
return;
}
// detect cases where one point is on the plane and the other two are on the same side
else if ((sa == SideOfPlane.ON && sb != SideOfPlane.ON && sb == sc) ||
(sb == SideOfPlane.ON && sa != SideOfPlane.ON && sa == sc) ||
(sc == SideOfPlane.ON && sa != SideOfPlane.ON && sa == sb))
{
return;
}
// keep in mind that intersection points are shared by both
// the upper HULL and lower HULL hence they lie perfectly
// on the plane that cut them
Vector3 qa;
Vector3 qb;
// check the cases where the points of the triangle actually lie on the plane itself
// in these cases, there is only going to be 2 triangles, one for the upper HULL and
// the other on the lower HULL
// we just need to figure out which points to accept into the upper or lower hulls.
if (sa == SideOfPlane.ON)
{
// if the point a is on the plane, test line b-c
if (Intersector.Intersect(pl, b, c, out qa))
{
// line b-c intersected, construct out triangles and return approprietly
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(a);
// our two generated triangles, we need to figure out which
// triangle goes into the UPPER hull and which goes into the LOWER hull
Triangle ta = new Triangle(a, b, qa);
Triangle tb = new Triangle(a, qa, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pq = tri.GenerateUV(qa);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pb, pq);
tb.SetUV(pa, pq, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pq = tri.GenerateNormal(qa);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pb, pq);
tb.SetNormal(pa, pq, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pq = tri.GenerateTangent(qa);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pb, pq);
tb.SetTangent(pa, pq, pc);
}
// b point lies on the upside of the plane
if (sb == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb);
}
// b point lies on the downside of the plane
else if (sb == SideOfPlane.DOWN)
{
result.AddUpperHull(tb).AddLowerHull(ta);
}
}
}
// test the case where the b point lies on the plane itself
else if (sb == SideOfPlane.ON)
{
// if the point b is on the plane, test line a-c
if (Intersector.Intersect(pl, a, c, out qa))
{
// line a-c intersected, construct out triangles and return approprietly
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(b);
// our two generated triangles, we need to figure out which
// triangle goes into the UPPER hull and which goes into the LOWER hull
Triangle ta = new Triangle(a, b, qa);
Triangle tb = new Triangle(qa, b, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pq = tri.GenerateUV(qa);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pb, pq);
tb.SetUV(pq, pb, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pq = tri.GenerateNormal(qa);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pb, pq);
tb.SetNormal(pq, pb, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pq = tri.GenerateTangent(qa);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pb, pq);
tb.SetTangent(pq, pb, pc);
}
// a point lies on the upside of the plane
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb);
}
// a point lies on the downside of the plane
else if (sa == SideOfPlane.DOWN)
{
result.AddUpperHull(tb).AddLowerHull(ta);
}
}
}
// test the case where the c point lies on the plane itself
else if (sc == SideOfPlane.ON)
{
// if the point c is on the plane, test line a-b
if (Intersector.Intersect(pl, a, b, out qa))
{
// line a-c intersected, construct out triangles and return approprietly
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(c);
// our two generated triangles, we need to figure out which
// triangle goes into the UPPER hull and which goes into the LOWER hull
Triangle ta = new Triangle(a, qa, c);
Triangle tb = new Triangle(qa, b, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pq = tri.GenerateUV(qa);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pq, pc);
tb.SetUV(pq, pb, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pq = tri.GenerateNormal(qa);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pq, pc);
tb.SetNormal(pq, pb, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pq = tri.GenerateTangent(qa);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pq, pc);
tb.SetTangent(pq, pb, pc);
}
// a point lies on the upside of the plane
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb);
}
// a point lies on the downside of the plane
else if (sa == SideOfPlane.DOWN)
{
result.AddUpperHull(tb).AddLowerHull(ta);
}
}
}
// at this point, all edge cases have been tested and failed, we need to perform
// full intersection tests against the lines. From this point onwards we will generate
// 3 triangles
else if (sa != sb && Intersector.Intersect(pl, a, b, out qa))
{
// intersection found against a - b
result.AddIntersectionPoint(qa);
// since intersection was found against a - b, we need to check which other
// lines to check (we only need to check one more line) for intersection.
// the line we check against will be the line against the point which lies on
// the other side of the plane.
if (sa == sc)
{
// we likely have an intersection against line b-c which will complete this loop
if (Intersector.Intersect(pl, b, 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(qa, b, qb);
Triangle tb = new Triangle(a, qa, qb);
Triangle tc = new Triangle(a, qb, 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(pqa, pb, pqb);
tb.SetUV(pa, pqa, pqb);
tc.SetUV(pa, pqb, 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(pqa, pb, pqb);
tb.SetNormal(pa, pqa, pqb);
tc.SetNormal(pa, pqb, 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(pqa, pb, pqb);
tb.SetTangent(pa, pqa, pqb);
tc.SetTangent(pa, pqb, pc);
}
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(tb).AddUpperHull(tc).AddLowerHull(ta);
}
else
{
result.AddLowerHull(tb).AddLowerHull(tc).AddUpperHull(ta);
}
}
}
else
{
// in this scenario, the point a is a "lone" point which lies in either upper
// or lower HULL. We need to perform another intersection to find the last point
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);
}
}
}
/**
* Perform an intersection between Plane and Line, storing intersection point
* in reference q. Function returns true if intersection has been found or
* false otherwise.
*/
public static bool Intersect(Plane pl, Line ln, out Vector3 q)
{
return(Intersector.Intersect(pl, ln.positionA, ln.positionB, out q));
}
/**
* Helper function to split this triangle by the provided plane and store
* the results inside the IntersectionResult structure.
* Returns true on success or false otherwise
*/
public bool Split(Plane pl, IntersectionResult result)
{
Intersector.Intersect(pl, this, result);
return(result.isValid);
}
