public static CSGPlane InverseTransformed(CSGPlane plane, Matrix4x4 transformation)
{
var ttrans = transformation.transpose;
var vector = ttrans * new Vector4(plane.a, plane.b, plane.c, -plane.d);
return(new CSGPlane(vector.x, vector.y, vector.z, -vector.w));
}
//public Plane() { }
public CSGPlane(CSGPlane inPlane)
{
a = inPlane.a;
b = inPlane.b;
c = inPlane.c;
d = inPlane.d;
}
public static CSGPlane Translated(CSGPlane plane, float translateX, float translateY, float translateZ)
{
return(new CSGPlane(plane.a, plane.b, plane.c,
// translated offset = plane.Normal.Dotproduct(translation)
// normal = A,B,C
plane.d + (plane.a * translateX) +
(plane.b * translateY) +
(plane.c * translateZ)));
}
public static CSGPlane Translated(CSGPlane plane, Vector3 translation)
{
return(new CSGPlane(plane.a, plane.b, plane.c,
// translated offset = plane.Normal.Dotproduct(translation)
// normal = A,B,C
plane.d + (plane.a * translation.x) +
(plane.b * translation.y) +
(plane.c * translation.z)));
}
public static CSGPlane InverseTransform(CSGPlane srcPlane, Matrix4x4 transformation)
{
var ittrans = transformation.transpose;
var vector = ittrans * new Vector4(srcPlane.a, srcPlane.b, srcPlane.c, -srcPlane.d);
var dstPlane = new CSGPlane(vector.x, vector.y, vector.z, -vector.w);
dstPlane.Normalize();
return(dstPlane);
}
public static void Transform(CSGPlane[] planes, Matrix4x4 transformation)
{
var ittrans = transformation.inverse.transpose;
for (int i = 0; i < planes.Length; i++)
{
var plane = planes[i];
var vector = ittrans * new Vector4(plane.a, plane.b, plane.c, -plane.d);
planes[i] = new CSGPlane(vector.x, vector.y, vector.z, -vector.w);
}
}
public static void Translate(CSGPlane[] src, Vector3 translation, out CSGPlane[] dst)
{
dst = new CSGPlane[src.Length];
for (int i = 0; i < src.Length; i++)
{
var plane = src[i];
dst[i] = new CSGPlane(plane.a, plane.b, plane.c,
plane.d + (plane.a * translation.x) +
(plane.b * translation.y) +
(plane.c * translation.z));
}
}
public static void Transform(List <CSGPlane> src, Matrix4x4 transformation, out CSGPlane[] dst)
{
var ittrans = transformation.inverse.transpose;
dst = new CSGPlane[src.Count];
for (int i = 0; i < src.Count; i++)
{
var plane = src[i];
var vector = ittrans * new Vector4(plane.a, plane.b, plane.c, -plane.d);
dst[i] = new CSGPlane(vector.x, vector.y, vector.z, -vector.w);
}
}
public static void InverseTransform(List <CSGPlane> srcPlanes, Matrix4x4 transformation, out CSGPlane[] dstPlanes)
{
var ittrans = transformation.transpose;
dstPlanes = new CSGPlane[srcPlanes.Count];
for (int i = 0; i < srcPlanes.Count; i++)
{
var plane = srcPlanes[i];
var vector = ittrans * new Vector4(plane.a, plane.b, plane.c, -plane.d);
dstPlanes[i] = new CSGPlane(vector.x, vector.y, vector.z, -vector.w);
dstPlanes[i].Normalize();
}
}
public PlaneAlignment Alignment(CSGPlane other)
{
var absDeltaA = Mathf.Abs(a - other.a);
var absDeltaB = Mathf.Abs(b - other.b);
var absDeltaC = Mathf.Abs(c - other.c);
if (float.IsNaN(absDeltaA) || float.IsInfinity(absDeltaA) ||
float.IsNaN(absDeltaB) || float.IsInfinity(absDeltaB) ||
float.IsNaN(absDeltaC) || float.IsInfinity(absDeltaC))
{
return(PlaneAlignment.Invalid);
}
if (absDeltaA > MathConstants.NormalEpsilon ||
absDeltaB > MathConstants.NormalEpsilon ||
absDeltaC > MathConstants.NormalEpsilon)
{
return(PlaneAlignment.Intersecting);
}
var isAligned = Vector3.Dot(normal, other.normal) >= 0;
var distance = Distance(other.pointOnPlane);
if (isAligned)
{
// inPlane1 and inPlanr2 are both facing in the same direction
if (distance < MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointAndInFront); // inPlane1 is in front of inPlane2
}
if (distance > MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointAndBehind); // inPlane1 is behind inPlane2
}
return(PlaneAlignment.CoincidingFacingSameDirection); // 'this' is coinciding with 'other'
}
else
{
// inPlane1 and inPlanr2 are both facing in the opposite direction
if (distance < MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointFacingOutwards); // the planes are facing outwards
}
if (distance > MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointFacingInwards); // the planes are facing inwards
}
return(PlaneAlignment.CoincidingFacingOppositeDirection); // 'this' is coinciding with 'other'
}
}
public bool Equals(CSGPlane other)
{
if (System.Object.ReferenceEquals(this, other))
{
return(true);
}
if (System.Object.ReferenceEquals(other, null))
{
return(false);
}
return(Mathf.Abs(this.Distance(other.pointOnPlane)) <= MathConstants.DistanceEpsilon &&
Mathf.Abs(other.Distance(this.pointOnPlane)) <= MathConstants.DistanceEpsilon &&
Mathf.Abs(a - other.a) <= MathConstants.NormalEpsilon &&
Mathf.Abs(b - other.b) <= MathConstants.NormalEpsilon &&
Mathf.Abs(c - other.c) <= MathConstants.NormalEpsilon);
}
static public Vector3 Intersection(CSGPlane inPlane1,
CSGPlane inPlane2,
CSGPlane inPlane3)
{
// intersection point with 3 planes
// {
// x = -( c2*b1*d3-c2*b3*d1+b3*c1*d2+c3*b2*d1-b1*c3*d2-c1*b2*d3)/
// (-c2*b3*a1+c3*b2*a1-b1*c3*a2-c1*b2*a3+b3*c1*a2+c2*b1*a3),
// y = ( c3*a2*d1-c3*a1*d2-c2*a3*d1+d2*c1*a3-a2*c1*d3+c2*d3*a1)/
// (-c2*b3*a1+c3*b2*a1-b1*c3*a2-c1*b2*a3+b3*c1*a2+c2*b1*a3),
// z = -(-a2*b1*d3+a2*b3*d1-a3*b2*d1+d3*b2*a1-d2*b3*a1+d2*b1*a3)/
// (-c2*b3*a1+c3*b2*a1-b1*c3*a2-c1*b2*a3+b3*c1*a2+c2*b1*a3)
// }
double bc1 = (inPlane1.b * inPlane3.c) - (inPlane3.b * inPlane1.c);
double bc2 = (inPlane2.b * inPlane1.c) - (inPlane1.b * inPlane2.c);
double bc3 = (inPlane3.b * inPlane2.c) - (inPlane2.b * inPlane3.c);
double ad1 = (inPlane1.a * inPlane3.d) - (inPlane3.a * inPlane1.d);
double ad2 = (inPlane2.a * inPlane1.d) - (inPlane1.a * inPlane2.d);
double ad3 = (inPlane3.a * inPlane2.d) - (inPlane2.a * inPlane3.d);
double x = -((inPlane1.d * bc3) + (inPlane2.d * bc1) + (inPlane3.d * bc2));
double y = -((inPlane1.c * ad3) + (inPlane2.c * ad1) + (inPlane3.c * ad2));
double z = +((inPlane1.b * ad3) + (inPlane2.b * ad1) + (inPlane3.b * ad2));
double w = -((inPlane1.a * bc3) + (inPlane2.a * bc1) + (inPlane3.a * bc2));
// better to have detectable invalid values than to have reaaaaaaally big values
if (w > -MathConstants.DistanceEpsilon &&
w < MathConstants.DistanceEpsilon)
{
return(new Vector3(Single.NaN,
Single.NaN,
Single.NaN));
}
else
{
return(new Vector3((float)(x / w),
(float)(y / w),
(float)(z / w)));
}
}
public static void InverseTransform(CSGPlane[] srcPlanes, Vector3[] srcTangents, Matrix4x4 transformation, out CSGPlane[] dstPlanes, out Vector3[] dstTangents)
{
var ittrans = transformation.transpose;
dstPlanes = new CSGPlane[srcPlanes.Length];
for (int i = 0; i < srcPlanes.Length; i++)
{
var plane = srcPlanes[i];
var vector = ittrans * new Vector4(plane.a, plane.b, plane.c, -plane.d);
dstPlanes[i] = new CSGPlane(vector.x, vector.y, vector.z, -vector.w);
}
dstTangents = new Vector3[srcTangents.Length];
for (int i = 0; i < srcTangents.Length; i++)
{
var tangent = srcTangents[i];
var vector = ittrans * new Vector4(tangent.x, tangent.y, tangent.z, 1);
dstTangents[i] = (new Vector3(vector.x / vector.w, vector.y / vector.w, vector.z / vector.w)).normalized;
}
}
public static PlaneAlignment TryIntersection(CSGPlane inPlane1, CSGPlane inPlane2, out Ray intersectionRay)
{
var lineDirection = Vector3.Cross(inPlane1.normal, inPlane2.normal);
var ax = Mathf.Abs(lineDirection.x);
var ay = Mathf.Abs(lineDirection.y);
var az = Mathf.Abs(lineDirection.z);
var aProduct = ax + ay + az;
if (float.IsNaN(aProduct) || float.IsInfinity(aProduct))
{
intersectionRay = MathConstants.emptyRay;
return(PlaneAlignment.Invalid);
}
if (aProduct < MathConstants.NormalEpsilon)
{
intersectionRay = MathConstants.emptyRay;
var isAligned = Mathf.Sign(Vector3.Dot(lineDirection, inPlane1.normal)) == Mathf.Sign(Vector3.Dot(lineDirection, inPlane2.normal));
var distance = inPlane1.Distance(inPlane2.pointOnPlane);
if (isAligned)
{
// inPlane1 and inPlane2 are both facing in the same direction
if (distance > MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointAndInFront); // inPlane1 is in front of inPlane2
}
if (distance < MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointAndBehind); // inPlane1 is behind inPlane2
}
return(PlaneAlignment.CoincidingFacingSameDirection); // 'this' is coinciding with 'other'
}
else
{
// inPlane1 and inPlane2 are both facing in the opposite direction
if (distance > MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointFacingOutwards); // the planes are facing outwards
}
if (distance < MathConstants.DistanceEpsilon)
{
return(PlaneAlignment.DisjointFacingInwards); // the planes are facing inwards
}
return(PlaneAlignment.CoincidingFacingOppositeDirection); // 'this' is coinciding with 'other'
}
}
var point = MathConstants.zeroVector3;
if (ax > ay)
{
if (ax > az) // x = 0
{
point.y = (-inPlane2.d * inPlane1.c + inPlane1.d * inPlane2.c) / lineDirection.x;
point.z = (-inPlane1.d * inPlane2.b + inPlane2.d * inPlane1.b) / lineDirection.x;
intersectionRay = new Ray(point, lineDirection);
return(PlaneAlignment.Intersecting);
}
}
else
{
if (ay > az) // y = 0
{
point.x = (-inPlane1.d * inPlane2.c + inPlane2.d * inPlane1.c) / lineDirection.y;
point.z = (-inPlane2.d * inPlane1.a + inPlane1.d * inPlane2.a) / lineDirection.y;
intersectionRay = new Ray(point, lineDirection);
return(PlaneAlignment.Intersecting);
}
}
// z = 0
{
point.x = (-inPlane2.d * inPlane1.b + inPlane1.d * inPlane2.b) / lineDirection.z;
point.y = (-inPlane1.d * inPlane2.a + inPlane2.d * inPlane1.a) / lineDirection.z;
intersectionRay = new Ray(point, lineDirection);
return(PlaneAlignment.Intersecting);
}
}
static public Vector3 Intersection(CSGPlane inPlane1,
CSGPlane inPlane2,
CSGPlane inPlane3)
{
/*
* var lineDirection = Vector3.Cross(inPlane1.normal, inPlane2.normal);
*
* if (float.IsNaN(lineDirection.x) || float.IsInfinity(lineDirection.x) ||
* float.IsNaN(lineDirection.y) || float.IsInfinity(lineDirection.y) ||
* float.IsNaN(lineDirection.z) || float.IsInfinity(lineDirection.z))
* return MathConstants.NaNVector3;
*
* float ax = Mathf.Abs(lineDirection.x);
* float ay = Mathf.Abs(lineDirection.y);
* float az = Mathf.Abs(lineDirection.z);
* int maxc = 3;
* if (ax > ay)
* {
* if (ax > az) maxc = 1;
* } else
* {
* if (ay > az) maxc = 2;
* }
*
* Vector3 linePosition;
* switch (maxc)
* { // select max coordinate
* default:
* case 1: // intersect with x=0
* linePosition.x = 0;
* linePosition.y = (-inPlane2.d * inPlane1.normal.z + inPlane1.d * inPlane2.normal.z) / lineDirection.x;
* linePosition.z = (-inPlane1.d * inPlane2.normal.y + inPlane2.d * inPlane1.normal.y) / lineDirection.x;
* break;
* case 2: // intersect with y=0
* linePosition.x = (-inPlane1.d * inPlane2.normal.z + inPlane2.d * inPlane1.normal.z) / lineDirection.y;
* linePosition.y = 0;
* linePosition.z = (-inPlane2.d * inPlane1.normal.x + inPlane1.d * inPlane2.normal.x) / lineDirection.y;
* break;
* case 3: // intersect with z=0
* linePosition.x = (-inPlane2.d * inPlane1.normal.y + inPlane1.d * inPlane2.normal.y) / lineDirection.z;
* linePosition.y = (-inPlane1.d * inPlane2.normal.x + inPlane2.d * inPlane1.normal.x) / lineDirection.z;
* linePosition.z = 0;
* break;
* }
*
* if (float.IsNaN(linePosition.x) || float.IsInfinity(linePosition.x) ||
* float.IsNaN(linePosition.y) || float.IsInfinity(linePosition.y) ||
* float.IsNaN(linePosition.z) || float.IsInfinity(linePosition.z))
* return MathConstants.NaNVector3;
*
* float denom = Vector3.Dot(inPlane3.normal, lineDirection);
*
* Vector3 p0l0 = inPlane3.pointOnPlane - linePosition;
* var t = Vector3.Dot(p0l0, inPlane3.normal) / denom;
*
* if (float.IsNaN(t) || float.IsInfinity(t))
* return MathConstants.NaNVector3;
*
* return (t * lineDirection) + linePosition;
* //*/
/*
* // intersection point with 3 planes
* // {
* // x = -( c2*b1*d3-c2*b3*d1+b3*c1*d2+c3*b2*d1-b1*c3*d2-c1*b2*d3)/
* // (-c2*b3*a1+c3*b2*a1-b1*c3*a2-c1*b2*a3+b3*c1*a2+c2*b1*a3),
* // y = ( c3*a2*d1-c3*a1*d2-c2*a3*d1+d2*c1*a3-a2*c1*d3+c2*d3*a1)/
* // (-c2*b3*a1+c3*b2*a1-b1*c3*a2-c1*b2*a3+b3*c1*a2+c2*b1*a3),
* // z = -(-a2*b1*d3+a2*b3*d1-a3*b2*d1+d3*b2*a1-d2*b3*a1+d2*b1*a3)/
* // (-c2*b3*a1+c3*b2*a1-b1*c3*a2-c1*b2*a3+b3*c1*a2+c2*b1*a3)
* // }
*
* var plane1a = (double)inPlane1.a;
* var plane1b = (double)inPlane1.b;
* var plane1c = (double)inPlane1.c;
* var plane1d = (double)inPlane1.d;
*
* var plane2a = (double)inPlane2.a;
* var plane2b = (double)inPlane2.b;
* var plane2c = (double)inPlane2.c;
* var plane2d = (double)inPlane2.d;
*
* var plane3a = (double)inPlane3.a;
* var plane3b = (double)inPlane3.b;
* var plane3c = (double)inPlane3.c;
* var plane3d = (double)inPlane3.d;
*
*
* var bc1 = (plane1b * plane3c) - (plane3b * plane1c);
* var bc2 = (plane2b * plane1c) - (plane1b * plane2c);
* var bc3 = (plane3b * plane2c) - (plane2b * plane3c);
*
* var w = -((plane1a * bc3) + (plane2a * bc1) + (plane3a * bc2));
*
* // better to have detectable invalid values than to have reaaaaaaally big values
* if (double.IsNaN(w) || double.IsInfinity(w) ||
* (w > -MathConstants.DistanceEpsilon &&
* w < MathConstants.DistanceEpsilon))
* {
* return MathConstants.NaNVector3;
* }
*
* var ad1 = (plane1a * plane3d) - (plane3a * plane1d);
* var ad2 = (plane2a * plane1d) - (plane1a * plane2d);
* var ad3 = (plane3a * plane2d) - (plane2a * plane3d);
*
* var x = -((plane1d * bc3) + (plane2d * bc1) + (plane3d * bc2));
* var y = -((plane1c * ad3) + (plane2c * ad1) + (plane3c * ad2));
* var z = +((plane1b * ad3) + (plane2b * ad1) + (plane3b * ad2));
*
* x /= w;
* y /= w;
* z /= w;
*
* var result = new Vector3((float)x, (float)y, (float)z);
* if (float.IsNaN(result.x) || float.IsInfinity(result.x) ||
* float.IsNaN(result.y) || float.IsInfinity(result.y) ||
* float.IsNaN(result.z) || float.IsInfinity(result.z))
* {
* return MathConstants.NaNVector3;
* }
*
* return result;
*
* //*/
//*
try
{
var plane1a = (decimal)inPlane1.a;
var plane1b = (decimal)inPlane1.b;
var plane1c = (decimal)inPlane1.c;
var plane1d = (decimal)inPlane1.d;
var plane2a = (decimal)inPlane2.a;
var plane2b = (decimal)inPlane2.b;
var plane2c = (decimal)inPlane2.c;
var plane2d = (decimal)inPlane2.d;
var plane3a = (decimal)inPlane3.a;
var plane3b = (decimal)inPlane3.b;
var plane3c = (decimal)inPlane3.c;
var plane3d = (decimal)inPlane3.d;
var bc1 = (plane1b * plane3c) - (plane3b * plane1c);
var bc2 = (plane2b * plane1c) - (plane1b * plane2c);
var bc3 = (plane3b * plane2c) - (plane2b * plane3c);
var w = -((plane1a * bc3) + (plane2a * bc1) + (plane3a * bc2));
var ad1 = (plane1a * plane3d) - (plane3a * plane1d);
var ad2 = (plane2a * plane1d) - (plane1a * plane2d);
var ad3 = (plane3a * plane2d) - (plane2a * plane3d);
var x = -((plane1d * bc3) + (plane2d * bc1) + (plane3d * bc2));
var y = -((plane1c * ad3) + (plane2c * ad1) + (plane3c * ad2));
var z = +((plane1b * ad3) + (plane2b * ad1) + (plane3b * ad2));
x /= w;
y /= w;
z /= w;
var result = new Vector3((float)x, (float)y, (float)z);
if (float.IsNaN(result.x) || float.IsInfinity(result.x) ||
float.IsNaN(result.y) || float.IsInfinity(result.y) ||
float.IsNaN(result.z) || float.IsInfinity(result.z))
{
return(MathConstants.NaNVector3);
}
return(result);
}
catch
{
return(MathConstants.NaNVector3);
}
//*/
}