// Equals
public bool Equals(RigidTransform rhs)
{
return(rot.Equals(rhs.rot) && pos.Equals(rhs.pos));
}
/// <summary>
/// Function to render the intersection of a plane and a triangle
/// </summary>
/// <param name="height"></param>
/// <param name="vertices"></param>
/// <param name="crossSectionRenderer"></param>
public void crossSectTri(Unity.Mathematics.float3 point, Unity.Mathematics.float3 normalDirection,
Unity.Mathematics.float3[] vertices, UnityEngine.LineRenderer crossSectionRenderer)
{
//Vertices are organized in clockwise manner starting from top
//top vertex
Unity.Mathematics.float3 a = vertices[0];
//bottom right
Unity.Mathematics.float3 b = vertices[1];
//bottom left
Unity.Mathematics.float3 c = vertices[2];
//intermediate calculations
Unity.Mathematics.float3 ac_hat = (c - a) / UnityEngine.Vector3.Magnitude(c - a);
Unity.Mathematics.float3 ab_hat = (b - a) / UnityEngine.Vector3.Magnitude(b - a);
Unity.Mathematics.float3 bc_hat = (c - b) / UnityEngine.Vector3.Magnitude(c - b);
//points of intersection on each line segment
Unity.Mathematics.float3 ac_star = IMRE.Math.Operations.SegmentPlaneIntersection(a, c, point, normalDirection);
Unity.Mathematics.float3 ab_star = IMRE.Math.Operations.SegmentPlaneIntersection(a, b, point, normalDirection);
Unity.Mathematics.float3 bc_star = IMRE.Math.Operations.SegmentPlaneIntersection(b, c, point, normalDirection);
//boolean values for if intersection hits only a vertex of the triangle
bool ac_star_isEndpoint;
ac_star_isEndpoint = ac_star.Equals(a) || ac_star.Equals(c);
bool ab_star_isEndpoint;
ab_star_isEndpoint = ab_star.Equals(a) || ab_star.Equals(b);
bool bc_star_isEndpoint;
bc_star_isEndpoint = bc_star.Equals(c) || bc_star.Equals(c);
//booleans for if intersection hits somewhere on the segments
bool ac_star_onSegment = !ac_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
bool ab_star_onSegment = !ab_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
bool bc_star_onSegment = !bc_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
//track how many vertices the intersection hits
int endpointCount = 0;
if (ac_star_isEndpoint)
{
endpointCount++;
}
if (ab_star_isEndpoint)
{
endpointCount++;
}
if (bc_star_isEndpoint)
{
endpointCount++;
}
//If plane does not hit triangle
if (!(ab_star_onSegment || ac_star_onSegment || bc_star_onSegment))
{
crossSectionRenderer.enabled = false;
UnityEngine.Debug.Log("Line does not intersect with any of triangle sides.");
}
//intersection is a segment (edge) of the triangle
//the concept for choosing the right points of the cross section is the same for each of these subcases
//two unique endpoint values
else if (endpointCount >= 2 &&
(!ab_star.Equals(ac_star) || !ab_star.Equals(bc_star) || !ac_star.Equals(bc_star)))
{
crossSectionRenderer.enabled = true;
//if there are two unique values, pick two.
//drop the result for the edge which is within the plane
//tolerance accounts for rounding errors
float tolerance = .00001f;
if (Unity.Mathematics.math.dot(ab_hat, normalDirection) < tolerance)
{
crossSectionRenderer.SetPosition(0, a);
crossSectionRenderer.SetPosition(1, b);
}
else if (Unity.Mathematics.math.dot(ac_hat, normalDirection) < tolerance)
{
crossSectionRenderer.SetPosition(0, a);
crossSectionRenderer.SetPosition(1, c);
}
else if (Unity.Mathematics.math.dot(bc_hat, normalDirection) < tolerance)
{
crossSectionRenderer.SetPosition(0, b);
crossSectionRenderer.SetPosition(1, c);
}
else
{
Debug.LogWarning("Error in calculation of line plane intersection");
crossSectionRenderer.enabled = false;
}
}
//intersection hits one vertex on triangle and one of the segments
else if (endpointCount == 2 && ab_star.Equals(ac_star) || ab_star.Equals(bc_star) ||
ac_star.Equals(bc_star))
{
crossSectionRenderer.enabled = true;
//if point of intersection hits a, it must hit bc_star; same logic applies to remaining subcases
if (ab_star.Equals(ac_star))
{
crossSectionRenderer.SetPosition(0, a);
crossSectionRenderer.SetPosition(1, bc_star);
}
else if (ab_star.Equals(bc_star))
{
crossSectionRenderer.SetPosition(0, b);
crossSectionRenderer.SetPosition(1, ac_star);
}
else if (ac_star.Equals(bc_star))
{
crossSectionRenderer.SetPosition(0, c);
crossSectionRenderer.SetPosition(1, ab_star);
}
else
{
Debug.LogWarning("Error in calculation of line plane intersection");
crossSectionRenderer.enabled = false;
}
}
//intersection hits somewhere on two different segments of triangle; last remaining case
else
{
crossSectionRenderer.enabled = true;
//find out which two segments are intersected and use their calculated intersections
if (ac_star_onSegment && ab_star_onSegment)
{
crossSectionRenderer.SetPosition(0, ac_star);
crossSectionRenderer.SetPosition(1, ab_star);
}
else if (ac_star_onSegment && bc_star_onSegment)
{
crossSectionRenderer.SetPosition(0, ac_star);
crossSectionRenderer.SetPosition(1, bc_star);
}
else if (ab_star_onSegment && bc_star_onSegment)
{
crossSectionRenderer.SetPosition(0, ab_star);
crossSectionRenderer.SetPosition(1, bc_star);
}
else
{
Debug.LogWarning("Error in calculation of line plane intersection");
crossSectionRenderer.enabled = false;
}
}
}
public bool Equals(float3x2 rhs)
{
return(c0.Equals(rhs.c0) && c1.Equals(rhs.c1));
}
public bool Equals(float3x3 rhs)
{
return(c0.Equals(rhs.c0) && c1.Equals(rhs.c1) && c2.Equals(rhs.c2));
}
public bool Equals(RigidTransform x)
{
return(rot.Equals(x.rot) && pos.Equals(x.pos));
}
public bool Equals(MinMaxAABB other)
{
return(Min.Equals(Min) && Max.Equals(other.Max));
}
public bool Equals(AffineTransform rhs)
{
return(rs.Equals(rhs.rs) && t.Equals(rhs.t));
}
/// <summary>
/// Function to render the intersection of a plane and a square
/// </summary>
/// <param name="height"></param>
/// <param name="vertices"></param>
/// <param name="crossSectionRenderer"></param>
public void crossSectSquare(Unity.Mathematics.float3 point, Unity.Mathematics.float3 normalDirection,
float3[] vertices,
UnityEngine.LineRenderer crossSectionRenderer)
{
//Vertices are organized in clockwise manner starting from top left
//top left
Unity.Mathematics.float3 a = vertices[0];
//top right
Unity.Mathematics.float3 b = vertices[1];
//bottom right
Unity.Mathematics.float3 c = vertices[2];
//bottom left
Unity.Mathematics.float3 d = vertices[3];
//intermediate calculations
Unity.Mathematics.float3 ab_hat = (b - a) / UnityEngine.Vector3.Magnitude(b - a);
Unity.Mathematics.float3 bc_hat = (c - b) / UnityEngine.Vector3.Magnitude(c - b);
Unity.Mathematics.float3 cd_hat = (d - c) / UnityEngine.Vector3.Magnitude(d - c);
Unity.Mathematics.float3 da_hat = (a - d) / UnityEngine.Vector3.Magnitude(a - d);
//calculations for point of intersection on different segments
Unity.Mathematics.float3 ab_star = IMRE.Math.Operations.SegmentPlaneIntersection(a, b, point, normalDirection);
Unity.Mathematics.float3 bc_star = IMRE.Math.Operations.SegmentPlaneIntersection(b, c, point, normalDirection);
Unity.Mathematics.float3 cd_star = IMRE.Math.Operations.SegmentPlaneIntersection(c, d, point, normalDirection);
Unity.Mathematics.float3 da_star = IMRE.Math.Operations.SegmentPlaneIntersection(d, a, point, normalDirection);
//booleans for if the intersection hits a vertex
bool ab_star_isEndpoint = ab_star.Equals(a) || ab_star.Equals(b);
bool bc_star_isEndpoint = bc_star.Equals(b) || bc_star.Equals(c);
bool cd_star_isEndpoint = cd_star.Equals(c) || cd_star.Equals(d);
bool da_star_isEndpoint = da_star.Equals(d) || da_star.Equals(a);
//booleans for if the intersection hits somewhere on the segments besides the vertices
bool ab_star_onSegment =
!ab_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
bool bc_star_onSegment =
!bc_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
bool cd_star_onSegment =
!cd_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
bool da_star_onSegment =
!da_star.Equals(new float3(Mathf.Infinity, Mathf.Infinity, Mathf.Infinity));
Debug.Log(ab_star);
Debug.Log(bc_star);
Debug.Log(cd_star);
Debug.Log(da_star);
//track how many vertices are hit in the intersection
int endpointCount = 0;
if (ab_star_isEndpoint)
{
endpointCount++;
}
if (bc_star_isEndpoint)
{
endpointCount++;
}
if (cd_star_isEndpoint)
{
endpointCount++;
}
if (da_star_isEndpoint)
{
endpointCount++;
}
//intersection does not hit triangle
if (!(ab_star_onSegment || bc_star_onSegment || cd_star_onSegment || da_star_onSegment))
{
crossSectionRenderer.enabled = false;
UnityEngine.Debug.Log("Line does not intersect with any of triangle sides.");
}
//intersection is an edge of the square
else if (endpointCount >= 2 &&
(!ab_star.Equals(bc_star) || !ab_star.Equals(da_star) || !bc_star.Equals(cd_star) ||
!cd_star.Equals(da_star)))
{
crossSectionRenderer.enabled = true;
//Case where edge is the intersection
//drop the two trivial cases, keep the two non-trivial cases.
UnityEngine.Vector3 result0 = ab_star;
UnityEngine.Vector3 result1 = cd_star;
if (result0.Equals(point) || result1.Equals(point))
{
//I know that the trivial cases are on opposite sides, because this is the case where the edge is the intersection.
//there are only two pairs of opposite sides. if it's not one, it's the other.
result0 = bc_star;
result1 = da_star;
crossSectionRenderer.SetPosition(0, result0);
crossSectionRenderer.SetPosition(1, result1);
}
else
{
Debug.LogWarning("Error in calculation of line plane intersection");
crossSectionRenderer.enabled = false;
}
}
//intersection hits one vertice and somewhere on a segment
else if (endpointCount == 2 &&
(ab_star.Equals(bc_star) || bc_star.Equals(cd_star) || cd_star.Equals(da_star)))
{
//find which vertex is in the intersection, and from there find which of the two possible segments are the other point of intersection
//the same logic carries through all of these subcases
if (ab_star.Equals(bc_star))
{
if (cd_star_onSegment)
{
crossSectionRenderer.SetPosition(0, b);
crossSectionRenderer.SetPosition(1, cd_star);
}
else
{
crossSectionRenderer.SetPosition(0, b);
crossSectionRenderer.SetPosition(1, da_star);
}
}
else if (bc_star.Equals(cd_star))
{
if (ab_star_onSegment)
{
crossSectionRenderer.SetPosition(0, c);
crossSectionRenderer.SetPosition(1, ab_star);
}
else
{
crossSectionRenderer.SetPosition(0, c);
crossSectionRenderer.SetPosition(1, da_star);
}
}
else if (cd_star.Equals(da_star))
{
if (ab_star_onSegment)
{
crossSectionRenderer.SetPosition(0, d);
crossSectionRenderer.SetPosition(1, ab_star);
}
else
{
crossSectionRenderer.SetPosition(0, c);
crossSectionRenderer.SetPosition(1, bc_star);
}
}
else if (da_star.Equals(ab_star))
{
if (cd_star_onSegment)
{
crossSectionRenderer.SetPosition(0, a);
crossSectionRenderer.SetPosition(1, cd_star);
}
if (bc_star_onSegment)
{
crossSectionRenderer.SetPosition(0, a);
crossSectionRenderer.SetPosition(1, bc_star);
}
}
else
{
Debug.LogWarning("Error in calculation of line plane intersection");
crossSectionRenderer.enabled = false;
}
}
//intersection hits two segments of the square
else
{
crossSectionRenderer.enabled = true;
//use booleans to determine which two segments are in the intersection
if (ab_star_onSegment && bc_star_onSegment)
{
crossSectionRenderer.SetPosition(0, ab_star);
crossSectionRenderer.SetPosition(1, bc_star);
}
else if (ab_star_onSegment && cd_star_onSegment)
{
crossSectionRenderer.SetPosition(0, ab_star);
crossSectionRenderer.SetPosition(1, cd_star);
}
else if (ab_star_onSegment && da_star_onSegment)
{
crossSectionRenderer.SetPosition(0, ab_star);
crossSectionRenderer.SetPosition(1, da_star);
}
else if (bc_star_onSegment && da_star_onSegment)
{
crossSectionRenderer.SetPosition(0, bc_star);
crossSectionRenderer.SetPosition(1, da_star);
}
else if (bc_star_onSegment && cd_star_onSegment)
{
crossSectionRenderer.SetPosition(0, bc_star);
crossSectionRenderer.SetPosition(1, cd_star);
}
else if (cd_star_onSegment && da_star_onSegment)
{
crossSectionRenderer.SetPosition(0, cd_star);
crossSectionRenderer.SetPosition(1, da_star);
}
else
{
Debug.LogWarning("Error in calculation of line plane intersection");
crossSectionRenderer.enabled = false;
}
}
}