using System;
using System.Collections.Generic;
namespace UnityEngine.ProBuilder
{
///
/// A collection of math functions that are useful when working with 3d meshes.
///
public static class Math
{
///
/// Pi / 2.
///
public const float phi = 1.618033988749895f;
///
/// ProBuilder epsilon constant.
///
const float k_FltEpsilon = float.Epsilon;
///
/// Epsilon to use when comparing vertex positions for equality.
///
const float k_FltCompareEpsilon = .0001f;
///
/// The minimum distance a handle must move on an axis before considering that axis as engaged.
///
internal const float handleEpsilon = .0001f;
///
/// Get a point on the circumference of a circle.
///
/// The radius of the circle.
/// Where along the circle should the point be projected. Angle is in degrees.
///
///
internal static Vector2 PointInCircumference(float radius, float angleInDegrees, Vector2 origin)
{
// Convert from degrees to radians via multiplication by PI/180
float x = (float)(radius * Mathf.Cos(Mathf.Deg2Rad * angleInDegrees)) + origin.x;
float y = (float)(radius * Mathf.Sin(Mathf.Deg2Rad * angleInDegrees)) + origin.y;
return new Vector2(x, y);
}
///
/// Provided a radius, latitudinal and longitudinal angle, return a position.
///
///
///
///
///
internal static Vector3 PointInSphere(float radius, float latitudeAngle, float longitudeAngle)
{
float x = (radius * Mathf.Cos(Mathf.Deg2Rad * latitudeAngle) * Mathf.Sin(Mathf.Deg2Rad * longitudeAngle));
float y = (radius * Mathf.Sin(Mathf.Deg2Rad * latitudeAngle) * Mathf.Sin(Mathf.Deg2Rad * longitudeAngle));
float z = (radius * Mathf.Cos(Mathf.Deg2Rad * longitudeAngle));
return new Vector3(x, y, z);
}
///
/// Find the signed angle from direction a to direction b.
///
/// The direction from which to rotate.
/// The direction to rotate towards.
/// A signed angle in degrees from direction a to direction b.
internal static float SignedAngle(Vector2 a, Vector2 b)
{
float t = Vector2.Angle(a, b);
if (b.x - a.x < 0)
t = 360f - t;
return t;
}
///
/// Squared distance between two points. This is the same as `(b - a).sqrMagnitude`.
///
/// First point.
/// Second point.
///
public static float SqrDistance(Vector3 a, Vector3 b)
{
float dx = b.x - a.x,
dy = b.y - a.y,
dz = b.z - a.z;
return dx * dx + dy * dy + dz * dz;
}
///
/// Get the area of a triangle.
///
/// http://www.iquilezles.org/blog/?p=1579
/// First vertex position of the triangle.
/// Second vertex position of the triangle.
/// Third vertex position of the triangle.
/// The area of the triangle.
public static float TriangleArea(Vector3 x, Vector3 y, Vector3 z)
{
float a = SqrDistance(x, y),
b = SqrDistance(y, z),
c = SqrDistance(z, x);
return Mathf.Sqrt((2f * a * b + 2f * b * c + 2f * c * a - a * a - b * b - c * c) / 16f);
}
///
/// Returns the Area of a polygon.
///
///
///
///
internal static float PolygonArea(Vector3[] vertices, int[] indexes)
{
float area = 0f;
for (int i = 0; i < indexes.Length; i += 3)
area += TriangleArea(vertices[indexes[i]], vertices[indexes[i + 1]], vertices[indexes[i + 2]]);
return area;
}
///
/// Returns a new point by rotating the Vector2 around an origin point.
///
/// Vector2 original point.
/// The pivot to rotate around.
/// How far to rotate in degrees.
///
internal static Vector2 RotateAroundPoint(this Vector2 v, Vector2 origin, float theta)
{
float cx = origin.x, cy = origin.y; // origin
float px = v.x, py = v.y; // point
float s = Mathf.Sin(theta * Mathf.Deg2Rad);
float c = Mathf.Cos(theta * Mathf.Deg2Rad);
// translate point back to origin:
px -= cx;
py -= cy;
// rotate point
float xnew = px * c + py * s;
float ynew = -px * s + py * c;
// translate point back:
px = xnew + cx;
py = ynew + cy;
return new Vector2(px, py);
}
///
/// Scales a Vector2 using origin as the pivot point.
///
///
///
///
///
public static Vector2 ScaleAroundPoint(this Vector2 v, Vector2 origin, Vector2 scale)
{
Vector2 tp = v - origin;
tp = Vector2.Scale(tp, scale);
tp += origin;
return tp;
}
///
/// Reflects a point across a line segment.
///
/// The point to reflect.
/// First point of the line segment.
/// Second point of the line segment.
/// The reflected point.
public static Vector2 ReflectPoint(Vector2 point, Vector2 lineStart, Vector2 lineEnd)
{
Vector2 line = lineEnd - lineStart;
Vector2 perp = new Vector2(-line.y, line.x); // skip normalize
float dist = Mathf.Sin(Vector2.Angle(line, point - lineStart) * Mathf.Deg2Rad) * Vector2.Distance(point, lineStart);
return point + perp * (dist * 2f) * (Vector2.Dot(point - lineStart, perp) > 0 ? -1f : 1f);
}
internal static float SqrDistanceRayPoint(Ray ray, Vector3 point)
{
return Vector3.Cross(ray.direction, point - ray.origin).sqrMagnitude;
}
///
/// Get the distance between a point and a finite line segment.
///
/// http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment
/// The point.
/// Line start.
/// Line end.
/// The distance from point to the nearest point on a line segment.
public static float DistancePointLineSegment(Vector2 point, Vector2 lineStart, Vector2 lineEnd)
{
// Return minimum distance between line segment vw and point p
float l2 = ((lineStart.x - lineEnd.x) * (lineStart.x - lineEnd.x)) + ((lineStart.y - lineEnd.y) * (lineStart.y - lineEnd.y)); // i.e. |w-v|^2 - avoid a sqrt
if (l2 == 0.0f) return Vector2.Distance(point, lineStart); // v == w case
// Consider the line extending the segment, parameterized as v + t (w - v).
// We find projection of point p onto the line.
// It falls where t = [(p-v) . (w-v)] / |w-v|^2
float t = Vector2.Dot(point - lineStart, lineEnd - lineStart) / l2;
if (t < 0.0)
return Vector2.Distance(point, lineStart); // Beyond the 'v' end of the segment
else if (t > 1.0)
return Vector2.Distance(point, lineEnd); // Beyond the 'w' end of the segment
Vector2 projection = lineStart + t * (lineEnd - lineStart); // Projection falls on the segment
return Vector2.Distance(point, projection);
}
///
/// Get the distance between a point and a finite line segment.
///
/// http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment
/// The point.
/// Line start.
/// Line end.
/// The distance from point to the nearest point on a line segment.
public static float DistancePointLineSegment(Vector3 point, Vector3 lineStart, Vector3 lineEnd)
{
// Return minimum distance between line segment vw and point p
float l2 = ((lineStart.x - lineEnd.x) * (lineStart.x - lineEnd.x)) + ((lineStart.y - lineEnd.y) * (lineStart.y - lineEnd.y)) + ((lineStart.z - lineEnd.z) * (lineStart.z - lineEnd.z)); // i.e. |w-v|^2 - avoid a sqrt
if (l2 == 0.0f) return Vector3.Distance(point, lineStart); // v == w case
// Consider the line extending the segment, parameterized as v + t (w - v).
// We find projection of point p onto the line.
// It falls where t = [(p-v) . (w-v)] / |w-v|^2
float t = Vector3.Dot(point - lineStart, lineEnd - lineStart) / l2;
if (t < 0.0)
return Vector3.Distance(point, lineStart); // Beyond the 'v' end of the segment
else if (t > 1.0)
return Vector3.Distance(point, lineEnd); // Beyond the 'w' end of the segment
Vector3 projection = lineStart + t * (lineEnd - lineStart); // Projection falls on the segment
return Vector3.Distance(point, projection);
}
///
/// Calculate the nearest point between two rays.
///
/// First ray.
/// Second ray.
///
public static Vector3 GetNearestPointRayRay(Ray a, Ray b)
{
return GetNearestPointRayRay(a.origin, a.direction, b.origin, b.direction);
}
internal static Vector3 GetNearestPointRayRay(Vector3 ao, Vector3 ad, Vector3 bo, Vector3 bd)
{
float dot = Vector3.Dot(ad, bd);
float abs = Mathf.Abs(dot);
// ray is parallel (or garbage)
if ((abs - 1f) > Mathf.Epsilon || abs < Mathf.Epsilon)
return ao;
Vector3 c = bo - ao;
float n = -dot * Vector3.Dot(bd, c) + Vector3.Dot(ad, c) * Vector3.Dot(bd, bd);
float d = Vector3.Dot(ad, ad) * Vector3.Dot(bd, bd) - dot * dot;
return ao + ad * (n / d);
}
// http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
// Returns 1 if the lines intersect, otherwise 0. In addition, if the lines
// intersect the intersection point may be stored in the intersect var
internal static bool GetLineSegmentIntersect(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, ref Vector2 intersect)
{
intersect = Vector2.zero;
Vector2 s1, s2;
s1.x = p1.x - p0.x; s1.y = p1.y - p0.y;
s2.x = p3.x - p2.x; s2.y = p3.y - p2.y;
float s, t;
s = (-s1.y * (p0.x - p2.x) + s1.x * (p0.y - p2.y)) / (-s2.x * s1.y + s1.x * s2.y);
t = (s2.x * (p0.y - p2.y) - s2.y * (p0.x - p2.x)) / (-s2.x * s1.y + s1.x * s2.y);
if (s >= 0 && s <= 1 && t >= 0 && t <= 1)
{
// Collision detected
intersect.x = p0.x + (t * s1.x);
intersect.y = p0.y + (t * s1.y);
return true;
}
return false;
}
///
/// True or false lines, do lines intersect.
///
///
///
///
///
///
internal static bool GetLineSegmentIntersect(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3)
{
Vector2 s1, s2;
s1.x = p1.x - p0.x; s1.y = p1.y - p0.y;
s2.x = p3.x - p2.x; s2.y = p3.y - p2.y;
float s, t;
s = (-s1.y * (p0.x - p2.x) + s1.x * (p0.y - p2.y)) / (-s2.x * s1.y + s1.x * s2.y);
t = (s2.x * (p0.y - p2.y) - s2.y * (p0.x - p2.x)) / (-s2.x * s1.y + s1.x * s2.y);
return (s >= 0 && s <= 1 && t >= 0 && t <= 1);
}
///
/// Casts a ray from outside the bounds to the polygon and checks how many edges are hit.
///
/// A series of individual edges composing a polygon. polygon length *must* be divisible by 2.
///
/// If present these indexes make up the border of polygon. If not, polygon is assumed to be in correct order.
/// True if the polygon contains point. False otherwise.
internal static bool PointInPolygon(Vector2[] polygon, Vector2 point, int[] indexes = null)
{
int len = indexes != null ? indexes.Length : polygon.Length;
if (len % 2 != 0)
{
Debug.LogError("PointInPolygon requires polygon indexes be divisible by 2!");
return false;
}
Bounds2D bounds = new Bounds2D(polygon, indexes);
if (bounds.ContainsPoint(point))
{
//Get the direction toward the first edge of the polygon
Vector2 p1 = polygon[indexes != null ? indexes[0] : 0];
Vector2 p2 = polygon[indexes != null ? indexes[1] : 1];
Vector2 center = p1 + (p2 - p1) * 0.5f;
Vector2 dir = center - bounds.center;
Vector2 rayStart = bounds.center + dir * (bounds.size.y + bounds.size.x + 2f);
int collisions = 0;
for (int i = 0; i < len; i += 2)
{
int a = indexes != null ? indexes[i] : i;
int b = indexes != null ? indexes[i + 1] : i + 1;
if (GetLineSegmentIntersect(rayStart, point, polygon[a], polygon[b]))
collisions++;
}
return collisions % 2 != 0;
}
else
return false;
}
///
/// Is the point within a polygon?
///
///
/// Assumes polygon has already been tested with AABB
///
///
///
///
///
///
internal static bool PointInPolygon(Vector2[] positions, Bounds2D polyBounds, Edge[] edges, Vector2 point)
{
int len = edges.Length * 2;
Vector2 rayStart = polyBounds.center + Vector2.up * (polyBounds.size.y + 2f);
int collisions = 0;
for (int i = 0; i < len; i += 2)
{
if (GetLineSegmentIntersect(rayStart, point, positions[i], positions[i + 1]))
collisions++;
}
return collisions % 2 != 0;
}
///
/// Is the 2d point within a 2d polygon? This overload is provided as a convenience for 2d arrays coming from cam.WorldToScreenPoint (which includes a Z value).
///
///
/// Assumes polygon has already been tested with AABB
///
///
///
///
///
///
internal static bool PointInPolygon(Vector3[] positions, Bounds2D polyBounds, Edge[] edges, Vector2 point)
{
int len = edges.Length * 2;
Vector2 rayStart = polyBounds.center + Vector2.up * (polyBounds.size.y + 2f);
int collisions = 0;
for (int i = 0; i < len; i += 2)
{
if (GetLineSegmentIntersect(rayStart, point, positions[i], positions[i + 1]))
collisions++;
}
return collisions % 2 != 0;
}
internal static bool RectIntersectsLineSegment(Rect rect, Vector2 a, Vector2 b)
{
return Clipping.RectContainsLineSegment(rect, a.x, a.y, b.x, b.y);
}
internal static bool RectIntersectsLineSegment(Rect rect, Vector3 a, Vector3 b)
{
return Clipping.RectContainsLineSegment(rect, a.x, a.y, b.x, b.y);
}
///
/// Test if a raycast intersects a triangle. Does not test for culling.
///
///
/// http://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm
/// http://www.cs.virginia.edu/~gfx/Courses/2003/ImageSynthesis/papers/Acceleration/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf
///
///
/// First vertex position in the triangle.
/// Second vertex position in the triangle.
/// Third vertex position in the triangle.
/// If triangle is intersected, this is the distance of intersection point from ray origin. Zero if not intersected.
/// If triangle is intersected, this is the point of collision. Zero if not intersected.
/// True if ray intersects, false if not.
public static bool RayIntersectsTriangle(Ray InRay, Vector3 InTriangleA, Vector3 InTriangleB, Vector3 InTriangleC,
out float OutDistance, out Vector3 OutPoint)
{
OutDistance = 0f;
OutPoint = Vector3.zero;
//Find vectors for two edges sharing V1
Vector3 e1 = InTriangleB - InTriangleA;
Vector3 e2 = InTriangleC - InTriangleA;
//Begin calculating determinant - also used to calculate `u` parameter
Vector3 P = Vector3.Cross(InRay.direction, e2);
//if determinant is near zero, ray lies in plane of triangle
float det = Vector3.Dot(e1, P);
// Non-culling branch
// {
if (det > -Mathf.Epsilon && det < Mathf.Epsilon)
return false;
float inv_det = 1f / det;
//calculate distance from V1 to ray origin
Vector3 T = InRay.origin - InTriangleA;
// Calculate u parameter and test bound
float u = Vector3.Dot(T, P) * inv_det;
//The intersection lies outside of the triangle
if (u < 0f || u > 1f)
return false;
//Prepare to test v parameter
Vector3 Q = Vector3.Cross(T, e1);
//Calculate V parameter and test bound
float v = Vector3.Dot(InRay.direction, Q) * inv_det;
//The intersection lies outside of the triangle
if (v < 0f || u + v > 1f)
return false;
float t = Vector3.Dot(e2, Q) * inv_det;
// }
if (t > Mathf.Epsilon)
{
//ray intersection
OutDistance = t;
OutPoint.x = (u * InTriangleB.x + v * InTriangleC.x + (1 - (u + v)) * InTriangleA.x);
OutPoint.y = (u * InTriangleB.y + v * InTriangleC.y + (1 - (u + v)) * InTriangleA.y);
OutPoint.z = (u * InTriangleB.z + v * InTriangleC.z + (1 - (u + v)) * InTriangleA.z);
return true;
}
return false;
}
// Temporary vector3 values
static Vector3 tv1, tv2, tv3, tv4;
///
/// Non-allocating version of Ray / Triangle intersection.
///
///
///
///
///
///
///
///
///
internal static bool RayIntersectsTriangle2(Vector3 origin,
Vector3 dir,
Vector3 vert0,
Vector3 vert1,
Vector3 vert2,
ref float distance,
ref Vector3 normal)
{
Math.Subtract(vert0, vert1, ref tv1);
Math.Subtract(vert0, vert2, ref tv2);
Math.Cross(dir, tv2, ref tv4);
float det = Vector3.Dot(tv1, tv4);
if (det < Mathf.Epsilon)
return false;
Math.Subtract(vert0, origin, ref tv3);
float u = Vector3.Dot(tv3, tv4);
if (u < 0f || u > det)
return false;
Math.Cross(tv3, tv1, ref tv4);
float v = Vector3.Dot(dir, tv4);
if (v < 0f || u + v > det)
return false;
distance = Vector3.Dot(tv2, tv4) * (1f / det);
Math.Cross(tv1, tv2, ref normal);
return true;
}
///
/// Return the secant of a radian.
/// Equivalent to: `1f / cos(x)`.
///
/// The radian to calculate the secant of.
/// The secant of radian x.
public static float Secant(float x)
{
return 1f / Mathf.Cos(x);
}
///
/// Calculate the unit vector normal of 3 points.
///
/// Equivalent to: `B-A x C-A`
///
/// First point of the triangle.
/// Second point of the triangle.
/// Third point of the triangle.
///
public static Vector3 Normal(Vector3 p0, Vector3 p1, Vector3 p2)
{
float ax = p1.x - p0.x,
ay = p1.y - p0.y,
az = p1.z - p0.z,
bx = p2.x - p0.x,
by = p2.y - p0.y,
bz = p2.z - p0.z;
Vector3 cross = Vector3.zero;
Cross(ax, ay, az, bx, by, bz, ref cross.x, ref cross.y, ref cross.z);
if (cross.magnitude < Mathf.Epsilon)
{
return new Vector3(0f, 0f, 0f); // bad triangle
}
else
{
cross.Normalize();
return cross;
}
}
///
/// Calculate the normal of a set of vertices. If indexes is null or not divisible by 3, the first 3 positions are used. If indexes is valid, an average of each set of 3 is taken.
///
///
///
///
internal static Vector3 Normal(IList vertices, IList indexes = null)
{
if (indexes == null || indexes.Count % 3 != 0)
{
Vector3 cross = Vector3.Cross(vertices[1].position - vertices[0].position, vertices[2].position - vertices[0].position);
cross.Normalize();
return cross;
}
else
{
int len = indexes.Count;
Vector3 nrm = Vector3.zero;
for (int i = 0; i < len; i += 3)
nrm += Normal(vertices[indexes[i]].position, vertices[indexes[i + 1]].position, vertices[indexes[i + 2]].position);
nrm /= (len / 3f);
nrm.Normalize();
return nrm;
}
}
///
/// Finds the best normal for a face.
///
/// The mesh that the target face belongs to.
/// The face to calculate a normal for.
/// A normal that most closely matches the face orientation in model corrdinates.
public static Vector3 Normal(ProBuilderMesh mesh, Face face)
{
if (mesh == null || face == null)
throw new ArgumentNullException("mesh");
var positions = mesh.positionsInternal;
// if the face is just a quad, use the first
// triangle normal.
// otherwise it's not safe to assume that the face
// has even generally uniform normals
Vector3 nrm = Normal(
positions[face.indexesInternal[0]],
positions[face.indexesInternal[1]],
positions[face.indexesInternal[2]]);
if (face.indexesInternal.Length > 6)
{
Vector3 prj = Projection.FindBestPlane(positions, face.distinctIndexesInternal).normal;
if (Vector3.Dot(nrm, prj) < 0f)
{
nrm.x = -prj.x;
nrm.y = -prj.y;
nrm.z = -prj.z;
}
else
{
nrm.x = prj.x;
nrm.y = prj.y;
nrm.z = prj.z;
}
}
return nrm;
}
///
/// Get the average normal of a set of individual triangles.
/// If p.Length % 3 == 0, finds the normal of each triangle in a face and returns the average. Otherwise return the normal of the first three points.
///
///
///
internal static Vector3 Normal(IList p)
{
if (p == null || p.Count < 3)
return Vector3.zero;
int c = p.Count;
if (c % 3 == 0)
{
Vector3 nrm = Vector3.zero;
for (int i = 0; i < c; i += 3)
nrm += Normal(p[i + 0], p[i + 1], p[i + 2]);
nrm /= (c / 3f);
nrm.Normalize();
return nrm;
}
Vector3 cross = Vector3.Cross(p[1] - p[0], p[2] - p[0]);
if (cross.magnitude < Mathf.Epsilon)
return new Vector3(0f, 0f, 0f); // bad triangle
return cross.normalized;
}
///
/// Returns the first normal, tangent, and bitangent for this face using the first triangle available for tangent and bitangent.
///
/// The mesh that the target face belongs to.
/// The face to calculate normal information for.
/// The normal, bitangent, and tangent for the face.
public static Normal NormalTangentBitangent(ProBuilderMesh mesh, Face face)
{
if (mesh == null || face == null || face.indexesInternal.Length < 3)
throw new System.ArgumentNullException("mesh", "Cannot find normal, tangent, and bitangent for null object, or faces with < 3 indexes.");
if (mesh.texturesInternal == null || mesh.texturesInternal.Length != mesh.vertexCount)
throw new ArgumentException("Mesh textures[0] channel is not present, cannot calculate tangents.");
var nrm = Math.Normal(mesh, face);
Vector3 tan1 = Vector3.zero;
Vector3 tan2 = Vector3.zero;
Vector4 tan = new Vector4(0f, 0f, 0f, 1f);
long i1 = face.indexesInternal[0];
long i2 = face.indexesInternal[1];
long i3 = face.indexesInternal[2];
Vector3 v1 = mesh.positionsInternal[i1];
Vector3 v2 = mesh.positionsInternal[i2];
Vector3 v3 = mesh.positionsInternal[i3];
Vector2 w1 = mesh.texturesInternal[i1];
Vector2 w2 = mesh.texturesInternal[i2];
Vector2 w3 = mesh.texturesInternal[i3];
float x1 = v2.x - v1.x;
float x2 = v3.x - v1.x;
float y1 = v2.y - v1.y;
float y2 = v3.y - v1.y;
float z1 = v2.z - v1.z;
float z2 = v3.z - v1.z;
float s1 = w2.x - w1.x;
float s2 = w3.x - w1.x;
float t1 = w2.y - w1.y;
float t2 = w3.y - w1.y;
float r = 1.0f / (s1 * t2 - s2 * t1);
Vector3 sdir = new Vector3((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
Vector3 tdir = new Vector3((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);
tan1 += sdir;
tan2 += tdir;
Vector3 n = nrm;
Vector3.OrthoNormalize(ref n, ref tan1);
tan.x = tan1.x;
tan.y = tan1.y;
tan.z = tan1.z;
tan.w = (Vector3.Dot(Vector3.Cross(n, tan1), tan2) < 0.0f) ? -1.0f : 1.0f;
return new Normal()
{
normal = nrm,
tangent = tan,
bitangent = Vector3.Cross(nrm, ((Vector3)tan) * tan.w)
};
}
///
/// Is the direction within epsilon of Up, Down, Left, Right, Forward, or Backwards?
///
///
///
///
internal static bool IsCardinalAxis(Vector3 v, float epsilon = k_FltEpsilon)
{
if (v == Vector3.zero)
return false;
v.Normalize();
return (1f - Mathf.Abs(Vector3.Dot(Vector3.up, v))) < epsilon ||
(1f - Mathf.Abs(Vector3.Dot(Vector3.forward, v))) < epsilon ||
(1f - Mathf.Abs(Vector3.Dot(Vector3.right, v))) < epsilon;
}
///
/// Component-wise division.
///
///
///
///
internal static Vector2 DivideBy(this Vector2 v, Vector2 o)
{
return new Vector2(v.x / o.x, v.y / o.y);
}
///
/// Component-wise division.
///
///
///
///
internal static Vector3 DivideBy(this Vector3 v, Vector3 o)
{
return new Vector3(v.x / o.x, v.y / o.y, v.z / o.z);
}
///
/// Find the largest value in an array.
///
///
///
///
internal static T Max(T[] array) where T : System.IComparable
{
if (array == null || array.Length < 1)
return default(T);
T max = array[0];
for (int i = 1; i < array.Length; i++)
if (array[i].CompareTo(max) >= 0)
max = array[i];
return max;
}
///
/// Find the smallest value in an array.
///
///
///
///
internal static T Min(T[] array) where T : System.IComparable
{
if (array == null || array.Length < 1)
return default(T);
T min = array[0];
for (int i = 1; i < array.Length; i++)
if (array[i].CompareTo(min) < 0)
min = array[i];
return min;
}
///
/// Return the largest axis in a Vector3.
///
///
///
internal static float LargestValue(Vector3 v)
{
if (v.x > v.y && v.x > v.z) return v.x;
if (v.y > v.x && v.y > v.z) return v.y;
return v.z;
}
///
/// Return the largest axis in a Vector2.
///
///
///
internal static float LargestValue(Vector2 v)
{
return (v.x > v.y) ? v.x : v.y;
}
///
/// The smallest X and Y value found in an array of Vector2. May or may not belong to the same Vector2.
///
///
///
internal static Vector2 SmallestVector2(Vector2[] v)
{
int len = v.Length;
Vector2 l = v[0];
for (int i = 0; i < len; i++)
{
if (v[i].x < l.x) l.x = v[i].x;
if (v[i].y < l.y) l.y = v[i].y;
}
return l;
}
///
/// The smallest X and Y value found in an array of Vector2. May or may not belong to the same Vector2.
///
///
/// Indexes of v array to test.
///
internal static Vector2 SmallestVector2(Vector2[] v, int[] indexes)
{
int len = indexes.Length;
Vector2 l = v[indexes[0]];
for (int i = 0; i < len; i++)
{
if (v[indexes[i]].x < l.x) l.x = v[indexes[i]].x;
if (v[indexes[i]].y < l.y) l.y = v[indexes[i]].y;
}
return l;
}
internal static Vector2 SmallestVector2(Vector2[] v, IList indexes)
{
int len = indexes.Count;
Vector2 l = v[indexes[0]];
for (int i = 0; i < len; i++)
{
if (v[indexes[i]].x < l.x) l.x = v[indexes[i]].x;
if (v[indexes[i]].y < l.y) l.y = v[indexes[i]].y;
}
return l;
}
///
/// The largest X and Y value in an array. May or may not belong to the same Vector2.
///
///
///
internal static Vector2 LargestVector2(Vector2[] v)
{
int len = v.Length;
Vector2 l = v[0];
for (int i = 0; i < len; i++)
{
if (v[i].x > l.x) l.x = v[i].x;
if (v[i].y > l.y) l.y = v[i].y;
}
return l;
}
internal static Vector2 LargestVector2(Vector2[] v, int[] indexes)
{
int len = indexes.Length;
Vector2 l = v[indexes[0]];
for (int i = 0; i < len; i++)
{
if (v[indexes[i]].x > l.x) l.x = v[indexes[i]].x;
if (v[indexes[i]].y > l.y) l.y = v[indexes[i]].y;
}
return l;
}
internal static Vector2 LargestVector2(Vector2[] v, IList indexes)
{
int len = indexes.Count;
Vector2 l = v[indexes[0]];
for (int i = 0; i < len; i++)
{
if (v[indexes[i]].x > l.x) l.x = v[indexes[i]].x;
if (v[indexes[i]].y > l.y) l.y = v[indexes[i]].y;
}
return l;
}
///
/// Creates an AABB with a set of vertices.
///
///
///
internal static Bounds GetBounds(Vector3[] positions, IList indices = null)
{
bool hasIndices = indices != null;
if ((hasIndices && indices.Count < 1) || positions.Length < 1)
return default(Bounds);
Vector3 min = positions[hasIndices ? indices[0] : 0];
Vector3 max = min;
if (hasIndices)
{
for (int i = 1, c = indices.Count; i < c; i++)
{
min.x = Mathf.Min(positions[indices[i]].x, min.x);
max.x = Mathf.Max(positions[indices[i]].x, max.x);
min.y = Mathf.Min(positions[indices[i]].y, min.y);
max.y = Mathf.Max(positions[indices[i]].y, max.y);
min.z = Mathf.Min(positions[indices[i]].z, min.z);
max.z = Mathf.Max(positions[indices[i]].z, max.z);
}
}
else
{
for (int i = 1, c = positions.Length; i < c; i++)
{
min.x = Mathf.Min(positions[i].x, min.x);
max.x = Mathf.Max(positions[i].x, max.x);
min.y = Mathf.Min(positions[i].y, min.y);
max.y = Mathf.Max(positions[i].y, max.y);
min.z = Mathf.Min(positions[i].z, min.z);
max.z = Mathf.Max(positions[i].z, max.z);
}
}
return new Bounds((min + max) * .5f, max - min);
}
///
/// Creates an AABB with a set of vertices.
///
///
///
internal static Bounds GetBounds(Vector3[] positions, IEnumerable faces)
{
bool initialized = false;
Vector3 min = Vector3.zero;
Vector3 max = min;
foreach (var face in faces)
{
var indices = face.distinctIndexesInternal;
if (!initialized)
{
initialized = true;
min = positions[indices[0]];
max = positions[indices[0]];
}
for (int i = 0, c = indices.Length; i < c; i++)
{
min.x = Mathf.Min(positions[indices[i]].x, min.x);
max.x = Mathf.Max(positions[indices[i]].x, max.x);
min.y = Mathf.Min(positions[indices[i]].y, min.y);
max.y = Mathf.Max(positions[indices[i]].y, max.y);
min.z = Mathf.Min(positions[indices[i]].z, min.z);
max.z = Mathf.Max(positions[indices[i]].z, max.z);
}
}
return new Bounds((min + max) * .5f, max - min);
}
static Vector3 ComponentMin(Vector3 a, Vector3 b)
{
return new Vector3(Mathf.Min(a.x, b.x), Mathf.Min(a.y, b.y), Mathf.Min(a.z, b.z));
}
static Vector3 ComponentMax(Vector3 a, Vector3 b)
{
return new Vector3(Mathf.Max(a.x, b.x), Mathf.Max(a.y, b.y), Mathf.Max(a.z, b.z));
}
///
/// Creates an AABB with a set of vertices.
///
///
///
internal static Bounds GetBounds(Vector3[] positions, IEnumerable edges)
{
bool initialized = false;
Vector3 min = Vector3.zero;
Vector3 max = min;
foreach (var edge in edges)
{
if (!initialized)
{
initialized = true;
min = positions[edge.a];
max = positions[edge.a];
}
min = ComponentMin(positions[edge.a], min);
max = ComponentMax(positions[edge.a], max);
min = ComponentMin(positions[edge.b], min);
max = ComponentMax(positions[edge.b], max);
}
return new Bounds((min + max) * .5f, max - min);
}
///
/// Gets the average of a vector array.
///
/// The array
/// If provided the average is the sum of all points contained in the indexes array. If not, the entire v array is used.
/// Average Vector3 of passed vertex array.
public static Vector2 Average(IList array, IList indexes = null)
{
if (array == null)
throw new ArgumentNullException("array");
Vector2 sum = Vector2.zero;
float len = indexes == null ? array.Count : indexes.Count;
if (indexes == null)
for (int i = 0; i < len; i++) sum += array[i];
else
for (int i = 0; i < len; i++) sum += array[indexes[i]];
return sum / len;
}
///
/// Gets the average of a vector array.
///
/// The array.
/// If provided the average is the sum of all points contained in the indexes array. If not, the entire v array is used.
/// Average Vector3 of passed vertex array.
public static Vector3 Average(IList array, IList indexes = null)
{
if (array == null)
throw new ArgumentNullException("array");
Vector3 sum = Vector3.zero;
float len = indexes == null ? array.Count : indexes.Count;
if (indexes == null)
{
for (int i = 0; i < len; i++)
{
sum.x += array[i].x;
sum.y += array[i].y;
sum.z += array[i].z;
}
}
else
{
for (int i = 0; i < len; i++)
{
sum.x += array[indexes[i]].x;
sum.y += array[indexes[i]].y;
sum.z += array[indexes[i]].z;
}
}
return sum / len;
}
///
/// Average a set of vertices.
///
/// The collection from which to select indices.
/// The function used to get vertex values.
///
///
///
internal static Vector3 Average(this IList list, Func selector, IList indexes = null)
{
if (list == null)
throw new ArgumentNullException("list");
if (selector == null)
throw new ArgumentNullException("selector");
Vector3 sum = Vector3.zero;
float len = indexes == null ? list.Count : indexes.Count;
if (indexes == null)
{
for (int i = 0; i < len; i++)
sum += selector(list[i]);
}
else
{
for (int i = 0; i < len; i++)
sum += selector(list[indexes[i]]);
}
return sum / len;
}
public static Vector4 Average(IList v, IList indexes = null)
{
Vector4 sum = Vector4.zero;
float len = indexes == null ? v.Count : indexes.Count;
if (indexes == null)
for (int i = 0; i < len; i++) sum += v[i];
else
for (int i = 0; i < len; i++) sum += v[indexes[i]];
return sum / len;
}
internal static Color Average(IList c, IList indexes = null)
{
Color sum = c[0];
float len = indexes == null ? c.Count : indexes.Count;
if (indexes == null)
for (int i = 1; i < len; i++) sum += c[i];
else
for (int i = 1; i < len; i++) sum += c[indexes[i]];
return sum / len;
}
///
/// Compares two Vector2 values component-wise, allowing for a margin of error.
///
/// First Vector2 value.
/// Second Vector2 value.
/// The maximum difference between components allowed.
/// True if a and b components are respectively within delta distance of one another.
internal static bool Approx2(this Vector2 a, Vector2 b, float delta = k_FltCompareEpsilon)
{
return
Mathf.Abs(a.x - b.x) < delta &&
Mathf.Abs(a.y - b.y) < delta;
}
///
/// Compares two Vector3 values component-wise, allowing for a margin of error.
///
/// First Vector3 value.
/// Second Vector3 value.
/// The maximum difference between components allowed.
/// True if a and b components are respectively within delta distance of one another.
internal static bool Approx3(this Vector3 a, Vector3 b, float delta = k_FltCompareEpsilon)
{
return
Mathf.Abs(a.x - b.x) < delta &&
Mathf.Abs(a.y - b.y) < delta &&
Mathf.Abs(a.z - b.z) < delta;
}
///
/// Compares two Vector4 values component-wise, allowing for a margin of error.
///
/// First Vector4 value.
/// Second Vector4 value.
/// The maximum difference between components allowed.
/// True if a and b components are respectively within delta distance of one another.
internal static bool Approx4(this Vector4 a, Vector4 b, float delta = k_FltCompareEpsilon)
{
return
Mathf.Abs(a.x - b.x) < delta &&
Mathf.Abs(a.y - b.y) < delta &&
Mathf.Abs(a.z - b.z) < delta &&
Mathf.Abs(a.w - b.w) < delta;
}
///
/// Compares two Color values component-wise, allowing for a margin of error.
///
/// First Color value.
/// Second Color value.
/// The maximum difference between components allowed.
/// True if a and b components are respectively within delta distance of one another.
internal static bool ApproxC(this Color a, Color b, float delta = k_FltCompareEpsilon)
{
return Mathf.Abs(a.r - b.r) < delta &&
Mathf.Abs(a.g - b.g) < delta &&
Mathf.Abs(a.b - b.b) < delta &&
Mathf.Abs(a.a - b.a) < delta;
}
///
/// Compares two float values component-wise, allowing for a margin of error.
///
/// First float value.
/// Second float value.
/// The maximum difference between components allowed.
/// True if a and b components are respectively within delta distance of one another.
internal static bool Approx(this float a, float b, float delta = k_FltCompareEpsilon)
{
return Mathf.Abs(b - a) < Mathf.Abs(delta);
}
///
/// Wrap value to range.
///
///
/// http://stackoverflow.com/questions/707370/clean-efficient-algorithm-for-wrapping-integers-in-c
///
///
///
///
///
internal static int Wrap(int value, int lowerBound, int upperBound)
{
int range_size = upperBound - lowerBound + 1;
if (value < lowerBound)
value += range_size * ((lowerBound - value) / range_size + 1);
return lowerBound + (value - lowerBound) % range_size;
}
///
/// Clamp a int to a range.
///
/// The value to clamp.
/// The lowest value that the clamped value can be.
/// The highest value that the clamped value can be.
/// A value clamped with the range of lowerBound and upperBound.
public static int Clamp(int value, int lowerBound, int upperBound)
{
return value upperBound ? upperBound : value;
}
internal static Vector3 ToSignedMask(this Vector3 vec, float delta = k_FltEpsilon)
{
return new Vector3(
Mathf.Abs(vec.x) > delta ? vec.x / Mathf.Abs(vec.x) : 0f,
Mathf.Abs(vec.y) > delta ? vec.y / Mathf.Abs(vec.y) : 0f,
Mathf.Abs(vec.z) > delta ? vec.z / Mathf.Abs(vec.z) : 0f
);
}
internal static Vector3 Abs(this Vector3 v)
{
return new Vector3(Mathf.Abs(v.x), Mathf.Abs(v.y), Mathf.Abs(v.z));
}
internal static int IntSum(this Vector3 mask)
{
return (int)Mathf.Abs(mask.x) + (int)Mathf.Abs(mask.y) + (int)Mathf.Abs(mask.z);
}
///
/// Non-allocating cross product.
///
///
/// `ref` does not box with primitive types (https://msdn.microsoft.com/en-us/library/14akc2c7.aspx)
///
///
///
///
///
///
internal static void Cross(Vector3 a, Vector3 b, ref float x, ref float y, ref float z)
{
x = a.y * b.z - a.z * b.y;
y = a.z * b.x - a.x * b.z;
z = a.x * b.y - a.y * b.x;
}
///
/// Non-allocating cross product.
///
///
///
///
internal static void Cross(Vector3 a, Vector3 b, ref Vector3 res)
{
res.x = a.y * b.z - a.z * b.y;
res.y = a.z * b.x - a.x * b.z;
res.z = a.x * b.y - a.y * b.x;
}
///
/// Non-allocating cross product.
///
///
///
///
///
///
///
///
///
///
internal static void Cross(float ax, float ay, float az, float bx, float by, float bz, ref float x, ref float y, ref float z)
{
x = ay * bz - az * by;
y = az * bx - ax * bz;
z = ax * by - ay * bx;
}
///
/// Vector subtraction without allocating a new vector.
///
///
///
///
internal static void Subtract(Vector3 a, Vector3 b, ref Vector3 res)
{
res.x = b.x - a.x;
res.y = b.y - a.y;
res.z = b.z - a.z;
}
internal static int Min(int a, int b)
{
return a < b ? a : b;
}
internal static int Max(int a, int b)
{
return a > b ? a : b;
}
internal static bool IsNumber(float value)
{
return !(float.IsInfinity(value) || float.IsNaN(value));
}
internal static bool IsNumber(Vector2 value)
{
return IsNumber(value.x) && IsNumber(value.y);
}
internal static bool IsNumber(Vector3 value)
{
return IsNumber(value.x) && IsNumber(value.y) && IsNumber(value.z);
}
internal static bool IsNumber(Vector4 value)
{
return IsNumber(value.x) && IsNumber(value.y) && IsNumber(value.z) && IsNumber(value.w);
}
internal static float MakeNonZero(float value, float min = .0001f)
{
if (float.IsNaN(value) || float.IsInfinity(value) || Mathf.Abs(value) < min)
return min * Mathf.Sign(value);
return value;
}
}
}