/// <summary>
/// Constructs a plane from 3 non-linear points on the plane, such that
/// Normal * p = Distance</summary>
/// <param name="p1">First point</param>
/// <param name="p2">Second point</param>
/// <param name="p3">Third point</param>
public Plane3F(Vec3F p1, Vec3F p2, Vec3F p3)
{
Vec3F d12 = p2 - p1;
Vec3F d13 = p3 - p1;
Vec3F normal = Vec3F.Cross(d12, d13);
Normal = Vec3F.Normalize(normal);
Distance = Vec3F.Dot(Normal, p1);
}
/// <summary>
/// Tests if any part of the polygon is inside this frustum. Errs on the side of inclusion.
/// The polygon and the frustum and the eye must be in the same space -- probably object space
/// to avoid the expense of transforming all the polygons into view space unnecessarily.</summary>
/// <param name="vertices">A polygon. Can be non-convex and non-planar for the frustum test.
/// Must be convex and planar for backface culling.</param>
/// <param name="eye">The camera's eye associated with this frustum. Is only used if 'backfaceCull'
/// is 'true'.</param>
/// <param name="backfaceCull">Should back-facing polygons always be excluded?</param>
/// <returns>True iff any part of the polygon is inside this frustum</returns>
public bool ContainsPolygon(Vec3F[] vertices, Vec3F eye, bool backfaceCull)
{
// If all of the points are outside any one plane, then the polygon is not contained.
for (int p = 0; p < 6; p++)
{
int v = 0;
for (; v < vertices.Length; v++)
{
float dist = m_planes[p].SignedDistance(vertices[v]);
if (dist > 0.0f)
{
break;
}
}
if (v == vertices.Length)
{
return(false);
}
}
if (backfaceCull)
{
// First calculate polygon normal, pointing "out from" the visible side.
Vec3F normal = new Vec3F();
for (int i = 2; i < vertices.Length; i++)
{
normal = Vec3F.Cross(vertices[0] - vertices[1],
vertices[i] - vertices[1]);
// Make sure that these 3 verts are not collinear
if (normal.LengthSquared != 0)
{
break;
}
}
// We can't use the near plane's normal, since it may no longer be pointing in the correct
// direction (due to non-uniform scalings, shear transforms, etc.).
if (Vec3F.Dot(normal, vertices[0] - eye) <= 0)
{
return(false);
}
}
// This is an approximation. To be absolutely sure, we'd have to test the 8 points
// of this frustum against the plane of the polygon and against the plane of each edge,
// perpendicular to the polygon plane.
return(true);
}
private Vec3F CalcTangent(Vec3F p1, Vec3F p2, Vec3F p3)
{
Vec3F v1 = (p1 - p2) / (p1 - p2).Length;
Vec3F v2 = (p3 - p2) / (p3 - p2).Length;
Vec3F bisector = v1 + v2;
Vec3F normal = Vec3F.Cross(v1, v2);
if (normal.Length < 0.1e-5f) // 3 points colinear
{
return(v2);
}
Vec3F tangent = Vec3F.Cross(normal, bisector);
tangent = tangent / tangent.Length;
return(tangent);
}
/// <summary>
/// Orthonormalizes the matrix</summary>
/// <param name="m">The matrix to orthonormalize</param>
public void OrthoNormalize(Matrix4F m)
{
Vec3F xAxis = new Vec3F(m.M11, m.M12, m.M13);
Vec3F yAxis = new Vec3F(m.M21, m.M22, m.M23);
Vec3F zAxis;
zAxis = Vec3F.Cross(xAxis, yAxis);
yAxis = Vec3F.Cross(zAxis, xAxis);
xAxis = xAxis / xAxis.Length;
yAxis = yAxis / yAxis.Length;
zAxis = zAxis / zAxis.Length;
M11 = xAxis.X; M12 = xAxis.Y; M13 = xAxis.Z;
M21 = yAxis.X; M22 = yAxis.Y; M23 = yAxis.Z;
M31 = zAxis.X; M32 = zAxis.Y; M33 = zAxis.Z;
M41 = m.M41;
M42 = m.M42;
M43 = m.M43;
}
public static void WritePolygon(
Vector3[] pts,
List <Vector3> pos, List <Vector3> normal, List <uint> indices)
{
// Calculate a normal for this face!
///////////////////////////////////////
// We have good C++ code for fitting planes to faces.
// But we don't have access to it from this code!
var n = new Vector3(0.0f, 0.0f, 0.0f);
for (uint c = 0; c < pts.Length - 2; ++c)
{
n += /*Vector3.Normalize*/ (Vector3.Cross(pts[c] - pts[c + 1], pts[c + 2] - pts[c + 1]));
}
// note that if we don't do the above normalize, then the contribution of
// each triangle will be weighted by the length of the cross product (which is
// proportional to the triangle area -- effectively weighting by triangle area).
n = -Vector3.Normalize(n);
var firstIndex = pos.Count;
for (uint c = 0; c < pts.Length; ++c)
{
pos.Add(pts[c]);
normal.Add(n);
}
for (uint c = 2; c < pts.Length; ++c)
{
indices.Add((uint)(firstIndex));
indices.Add((uint)(firstIndex + c - 1));
indices.Add((uint)(firstIndex + c));
}
}
public static void CreateCylinder(float rad1, float rad2, float height, uint slices, uint stacks,
List <Vector3> pos, List <Vector3> normal, List <uint> indices)
{
float stackHeight = height / stacks;
// Amount to increment radius as we move up each stack level from bottom to top.
float radiusStep = (rad2 - rad1) / stacks;
uint numRings = stacks + 1;
// Compute vertices for each stack ring.
for (uint i = 0; i < numRings; ++i)
{
float y = i * stackHeight;
float r = rad1 + i * radiusStep;
// Height and radius of next ring up.
float y_next = (i + 1) * stackHeight;
float r_next = rad1 + (i + 1) * radiusStep;
// vertices of ring
float dTheta = 2.0f * MathHelper.Pi / slices;
for (uint j = 0; j <= slices; ++j)
{
float c = (float)Math.Cos(j * dTheta);
float s = (float)Math.Sin(j * dTheta);
// tex coord if needed.
//float u = j/(float) slices;
//float v = 1.0f - (float) i/stacks;
// Partial derivative in theta direction to get tangent vector (this is a unit vector).
Vector3 T = new Vector3(-s, 0.0f, c);
// Compute tangent vector down the slope of the cone (if the top/bottom
// radii differ then we get a cone and not a true cylinder).
Vector3 P = new Vector3(r * c, y, r * s);
Vector3 P_next = new Vector3(r_next * c, y_next, r_next * s);
Vector3 B = P - P_next;
B.Normalize();
Vector3 N = Vector3.Cross(T, B);
N.Normalize();
P.Z *= -1;
N.Z *= -1;
pos.Add(P);
if (normal != null)
{
normal.Add(N);
}
}
}
uint numRingVertices = slices + 1;
// Compute indices for each stack.
for (uint i = 0; i < stacks; ++i)
{
for (uint j = 0; j < slices; ++j)
{
indices.Add(i * numRingVertices + j);
indices.Add((i + 1) * numRingVertices + j + 1);
indices.Add((i + 1) * numRingVertices + j);
indices.Add(i * numRingVertices + j);
indices.Add(i * numRingVertices + j + 1);
indices.Add((i + 1) * numRingVertices + j + 1);
}
}
// build bottom cap.
if (rad1 > 0)
{
uint baseIndex = (uint)pos.Count;
// Duplicate cap vertices because the texture coordinates and normals differ.
float y = 0;
// vertices of ring
float dTheta = 2.0f * MathHelper.Pi / slices;
for (uint i = 0; i <= slices; ++i)
{
float x = rad1 * (float)Math.Cos(i * dTheta);
float z = rad1 * (float)Math.Sin(i * dTheta);
// Map [-1,1]-->[0,1] for planar texture coordinates.
//float u = +0.5f * x / mBottomRadius + 0.5f;
//float v = -0.5f * z / mBottomRadius + 0.5f;
Vector3 p = new Vec3F(x, y, -z);
pos.Add(p);
if (normal != null)
{
normal.Add(new Vec3F(0.0f, -1.0f, 0.0f));
}
}
// cap center vertex
pos.Add(new Vec3F(0.0f, y, 0.0f));
if (normal != null)
{
normal.Add(new Vec3F(0.0f, -1.0f, 0.0f));
}
// tex coord for center cap 0.5f, 0.5f
// index of center vertex
uint centerIndex = (uint)pos.Count - 1;
for (uint i = 0; i < slices; ++i)
{
indices.Add(centerIndex);
indices.Add(baseIndex + i + 1);
indices.Add(baseIndex + i);
}
}
// build top cap.
if (rad2 > 0)
{
uint baseIndex = (uint)pos.Count;
// Duplicate cap vertices because the texture coordinates and normals differ.
float y = height;
// vertices of ring
float dTheta = 2.0f * MathHelper.Pi / slices;
for (uint i = 0; i <= slices; ++i)
{
float x = rad2 * (float)Math.Cos(i * dTheta);
float z = rad2 * (float)Math.Sin(i * dTheta);
// Map [-1,1]-->[0,1] for planar texture coordinates.
//float u = +0.5f * x / mTopRadius + 0.5f;
//float v = -0.5f * z / mTopRadius + 0.5f;
pos.Add(new Vec3F(x, y, -z));
if (normal != null)
{
normal.Add(new Vec3F(0.0f, 1.0f, 0.0f));
}
}
// pos, norm, tex1 for cap center vertex
pos.Add(new Vec3F(0.0f, y, 0.0f));
if (normal != null)
{
normal.Add(new Vec3F(0.0f, 1.0f, 0.0f));
}
// tex coord 0.5f, 0.5f
// index of center vertex
uint centerIndex = (uint)pos.Count - 1;
for (uint i = 0; i < slices; ++i)
{
indices.Add(centerIndex);
indices.Add(baseIndex + i);
indices.Add(baseIndex + i + 1);
}
}
}
private void CalcPlaneNormal(int planeIndex, Vec3F u1, Vec3F u2)
{
m_planes[planeIndex].Normal = Vec3F.Cross(u1, u2);
m_planes[planeIndex].Normal.Normalize();
m_planes[planeIndex].Distance = 0;
}
private bool IsLeftOf(TriVx v0, TriVx v1, TriVx v2, Vec3F normal)
{
Vec3F cross = Vec3F.Cross(v1.V - v0.V, v2.V - v0.V);
return(Vec3F.Dot(cross, normal) > 0.0f);
}
/// <summary>
/// Finds the intersection point of the ray with the given convex polygon, if any. Returns the nearest
/// vertex of the polygon to the intersection point. Can optionally backface cull the polygon.
/// For backface culling, the front of the polygon is considered to be the side that has
/// the vertices ordered counter-clockwise.</summary>
/// <param name="vertices">Polygon vertices</param>
/// <param name="intersectionPoint">Intersection point</param>
/// <param name="nearestVert">Nearest polygon vertex to the point of intersection</param>
/// <param name="normal">Normal unit-length vector, facing out from the side whose
/// vertices are ordered counter-clockwise</param>
/// <param name="backFaceCull">True if backface culling should be done</param>
/// <returns>True iff the ray intersects the polygon</returns>
public bool IntersectPolygon(Vec3F[] vertices, out Vec3F intersectionPoint,
out Vec3F nearestVert, out Vec3F normal, bool backFaceCull)
{
bool intersects = true;
int sign = 0;
normal = new Vec3F();
// First calc polygon normal
for (int i = 2; i < vertices.Length; i++)
{
normal = Vec3F.Cross(vertices[i] - vertices[1], vertices[0] - vertices[1]);
// Make sure that these 3 verts are not collinear
float lengthSquared = normal.LengthSquared;
if (lengthSquared != 0)
{
normal *= (1.0f / (float)Math.Sqrt(lengthSquared));
break;
}
}
if (backFaceCull)
{
if (Vec3F.Dot(normal, Direction) >= 0.0)
{
intersectionPoint = new Vec3F();
nearestVert = new Vec3F();
return(false);
}
}
// Build plane and check if the ray intersects the plane.
intersects = IntersectPlane(
new Plane3F(normal, vertices[1]),
out intersectionPoint);
// Now check all vertices against intersection point
for (int i = 0; i < vertices.Length && intersects; i++)
{
int i1 = i;
int i0 = (i == 0 ? vertices.Length - 1 : i - 1);
Vec3F cross = Vec3F.Cross(vertices[i1] - vertices[i0],
intersectionPoint - vertices[i0]);
// Check if edge and intersection vectors are collinear
if (cross.LengthSquared == 0.0f)
{
// check if point is on edge
intersects =
((vertices[i1] - vertices[i0]).LengthSquared >=
(intersectionPoint - vertices[i0]).LengthSquared);
break;
}
else
{
float dot = Vec3F.Dot(cross, normal);
if (i == 0)
{
sign = Math.Sign(dot);
}
else if (Math.Sign(dot) != sign)
{
intersects = false;
}
}
}
// if we have a definite intersection, find the closest snap-to vertex.
if (intersects)
{
nearestVert = vertices[0];
float nearestDistSqr = (intersectionPoint - nearestVert).LengthSquared;
for (int i = 1; i < vertices.Length; i++)
{
float distSqr = (vertices[i] - intersectionPoint).LengthSquared;
if (distSqr < nearestDistSqr)
{
nearestDistSqr = distSqr;
nearestVert = vertices[i];
}
}
}
else
{
nearestVert = s_blankPoint;
}
return(intersects);
}