public bool Equals(Ellipse other)
{
return(
Mathx.IsEqual(centre, other.centre) &&
Mathx.IsEqual(extents, other.extents)
);
}
public bool Equals(Range3Int other)
{
return(
Mathx.IsEqual(min, other.min) &&
Mathx.IsEqual(max, other.max)
);
}
public bool Equals(Line other)
{
return(
Mathx.IsEqual(v0, other.v0) &&
Mathx.IsEqual(v1, other.v1)
);
}
public bool Equals(LinearEquation other)
{
return(
Mathx.IsEqual(this.a, other.a) &&
Mathx.IsEqual(this.b, other.b)
);
}
/// <summary> Calculates rectangle vertices into 'target' array </summary>
public static void GetVertices(Vector2[] target, Vector2 position, Vector2 size, float angle)
{
for (int i = 0; i < Vertices.Length; ++i)
{
target[i] = Mathx.Transform(Vertices[i], position, angle, size);
}
}
public bool Equals(Sphere other)
{
return(
Mathx.IsEqual(centre, other.centre) &&
Mathx.IsEqual(radius, other.radius)
);
}
public bool Equals(Equation1 other)
{
return(
Mathx.IsEqual(this.x, other.x) &&
Mathx.IsEqual(this.y, other.y)
);
}
/// <summary> Attempts to calculate circle with center in 'c' and radius 'r' from three points </summary>
public static bool TryCreate(Vector2 v0, Vector2 v1, Vector2 v2, out Vector2 c, out float r)
{
c = default;
r = default;
var c1 = new Vector4(v0.x * v0.x + v0.y * v0.y, v1.x * v1.x + v1.y * v1.y, v2.x * v2.x + v2.y * v2.y, 0.0f);
var c2 = new Vector4(v0.x, v1.x, v2.x, 0.0f);
var c3 = new Vector4(v0.y, v1.y, v2.y, 0.0f);
var c4 = new Vector4(1.0f, 1.0f, 1.0f, 0.0f);
var c5 = new Vector4(0.0f, 0.0f, 0.0f, 1.0f);
var M11 = new Matrix4x4(c2, c3, c4, c5);
var M12 = new Matrix4x4(c1, c3, c4, c5);
var M13 = new Matrix4x4(c1, c2, c4, c5);
var M14 = new Matrix4x4(c1, c2, c3, c5);
var m11 = M11.determinant;
var m12 = M12.determinant;
var m13 = M13.determinant;
var m14 = M14.determinant;
if (Mathx.IsZero(m11))
{
return(false);
}
c.x = 0.5f * m12 / m11;
c.y = -0.5f * m13 / m11;
r = Mathf.Sqrt(c.x * c.x + c.y * c.y + m14 / m11);
return(true);
}
public bool Contains(Vector3Int otherMin, Vector3Int otherMax)
{
return(
Mathx.IsLesserOrEqual(min, otherMin) &&
Mathx.IsLesserOrEqual(otherMax, max)
);
}
/// <summary> Calculates rectangle vertices into 'target' array </summary>
public static void GetVertices(Vector3[] target, Vector3 position, Vector2 size, Quaternion rotation)
{
for (int i = 0; i < Vertices.Length; ++i)
{
target[i] = Mathx.Transform(Vertices[i], position, rotation, size);
}
}
public bool Overlaps(Range3Int other)
{
return(
Mathx.IsLesserOrEqual(min, other.max) &&
Mathx.IsLesserOrEqual(other.min, max)
);
}
public Range3Int Intersection(Range3Int other)
{
return(new Range3Int(
Mathx.Max(min, other.min),
Mathx.Min(max, other.max)
));
}
public bool Equals(Triangle other)
{
return(
Mathx.IsEqual(v0, other.v0) &&
Mathx.IsEqual(v1, other.v1) &&
Mathx.IsEqual(v2, other.v2)
);
}
public bool Equals(QuadraticEquation other)
{
return(
Mathx.IsEqual(this.a, other.a) &&
Mathx.IsEqual(this.b, other.b) &&
Mathx.IsEqual(this.c, other.c)
);
}
public static bool Contains(Vector3 v0, Vector3 v1, Vector3 p)
{
float v0v1 = (v1 - v0).sqrMagnitude;
float v0p = (p - v0).sqrMagnitude;
float pv1 = (v1 - p).sqrMagnitude;
return(Mathx.IsEqual(v0v1, v0p + pv1));
}
public bool Equals(SinEquation other)
{
return(
Mathx.IsEqual(this.dx, other.dx) &&
Mathx.IsEqual(this.sx, other.sx) &&
Mathx.IsEqual(this.dy, other.dy) &&
Mathx.IsEqual(this.sy, other.sy)
);
}
public static bool Contains(Vector3 v0, Vector3 v1, Vector3 v2, Vector3 p)
{
var bc = Barycenter(v0, v1, v2, p);
return(
Mathx.IsEqual(bc.x + bc.y + bc.z, 1.0f) &&
Mathx.IsInRange(bc, Vector3.zero, Vector3.one)
);
}
public bool Equals(Equation3 other)
{
return(
Mathx.IsEqual(this.x, other.x) &&
Mathx.IsEqual(this.y, other.y) &&
Mathx.IsEqual(this.z, other.z) &&
Mathx.IsEqual(this.w, other.w)
);
}
public static LinearEquation FromPoints(Vector2 A, Vector2 B)
{
if (Mathx.IsZero(A.x) && Mathx.IsZero(B.x))
{
return(invalid);
}
float a = (B.y - A.y) / (B.x - A.x);
float b = A.y - a * A.x;
return(new LinearEquation(a, b));
}
public static void GetNoiseMap(
float[][] map, int dx = 0, int dy = 0,
int octaves = 1, float persistance = 0.5f, float lacunarity = 2.0f,
float sx = 1.0f, float sy = 1.0f, int seed = 0
)
{
var random = new Random(seed);
var width = map.GetWidth();
var height = map.GetHeight();
var pmin = 0.0f;
var pmax = 1.0f;
for (uint i = 1; i < octaves; ++i)
{
var ppow = Mathx.Pow(persistance, i);
pmin += ppow * 0.25f;
pmax += ppow * 0.75f;
}
var rdx = random.NextFloat(-99999.0f, +99999.0f);
var rdy = random.NextFloat(-99999.0f, +99999.0f);
var fx = 1.0f / (sx * width);
var fy = 1.0f / (sy * height);
for (int y = 0; y < height; ++y)
{
for (int x = 0; x < width; ++x)
{
float amplitude = 1.0f;
float frequency = 1.0f;
float value = 0.0f;
for (int i = 0; i < octaves; ++i)
{
float sampleX = ((x - dx) * fx) * frequency + rdx;
float sampleY = ((y - dy) * fy) * frequency + rdy;
float pv = Mathf.PerlinNoise(sampleX, sampleY);
value += pv * amplitude;
amplitude *= persistance;
frequency *= lacunarity;
}
map[x][y] = Mathf.SmoothStep(pmin, pmax, value);
}
}
}
public static Color ToNormal(Vector3 v)
{
return(ToColor((Mathx.Add(v.XZY(), 1.0f)) * 0.5f));
}
/// <summary> Attempts to calculate a sphere with center in 'c' and radius 'r' from four points </summary>
public static bool TryCreate(Vector3 v0, Vector3 v1, Vector3 v2, Vector3 v3, out Vector3 c, out float r)
{
c = default;
r = default;
var p = new float[4, 4]
{
{ v0.x, v0.y, v0.z, 1.0f },
{ v1.x, v1.y, v1.z, 1.0f },
{ v2.x, v2.y, v2.z, 1.0f },
{ v3.x, v3.y, v3.z, 1.0f }
};
var a = new float[4, 4];
// Find minor 1, 1.
for (int i = 0; i < 4; i++)
{
a[i, 0] = p[i, 0];
a[i, 1] = p[i, 1];
a[i, 2] = p[i, 2];
}
float detM11 = Mathx.Determinant(a);
if (Mathx.IsZero(detM11))
{
return(false);
}
for (int i = 0; i < 4; i++)
{
a[i, 0] = p[i, 0] * p[i, 0] + p[i, 1] * p[i, 1] + p[i, 2] * p[i, 2];
}
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 1];
a[i, 2] = p[i, 2];
}
float detM12 = Mathx.Determinant(a);
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 0];
a[i, 2] = p[i, 2];
}
float detM13 = Mathx.Determinant(a);
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 0];
a[i, 2] = p[i, 1];
}
float detM14 = Mathx.Determinant(a);
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 0];
a[i, 2] = p[i, 1];
a[i, 3] = p[i, 2];
}
float detM15 = Mathx.Determinant(a);
c.x = 0.5f * detM12 / detM11;
c.y = -0.5f * detM13 / detM11;
c.z = 0.5f * detM14 / detM11;
r = Mathf.Sqrt(c.x * c.x + c.y * c.y + c.z * c.z - detM15 / detM11);
return(true);
}
public static float PerlinNoise(float x, float y, float z)
{
const float MOD = 289.0f;
const float PERMUTE = 34.0f;
Vector3 P = new Vector3(x, y, z);
Vector3 Pi0 = Mathx.Floor(P); // Integer part for indexing
Vector3 Pi1 = Pi0 + Vector3.one; // Integer part + 1
Pi0 = Mathx.Mod(Pi0, MOD);
Pi1 = Mathx.Mod(Pi1, MOD);
Vector3 Pf0 = Mathx.Frac(P); // Fractional part for interpolation
Vector3 Pf1 = Pf0 - Vector3.one; // Fractional part - 1.0
Vector4 ix = new Vector4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
Vector4 iy = new Vector4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
Vector4 iz0 = new Vector4(Pi0.z, Pi0.z, Pi0.z, Pi0.z);
Vector4 iz1 = new Vector4(Pi1.z, Pi1.z, Pi1.z, Pi1.z);
Vector4 ixy = Mathx.Permute(Mathx.Permute(ix, PERMUTE, MOD) + iy, PERMUTE, MOD);
Vector4 ixy0 = Mathx.Permute(ixy + iz0, PERMUTE, MOD);
Vector4 ixy1 = Mathx.Permute(ixy + iz1, PERMUTE, MOD);
Vector4 gx0 = ixy0 * (1.0f / 7.0f);
Vector4 gy0 = Mathx.Sub(Mathx.Frac(Mathx.Mul(Mathx.Floor(gx0), (1.0f / 7.0f))), 0.5f);
gx0 = Mathx.Frac(gx0);
Vector4 gz0 = Vector4.one * 0.5f - Mathx.Abs(gx0) - Mathx.Abs(gy0);
Vector4 sz0 = Mathx.Step(gz0, Vector4.zero);
gx0 -= Mathx.Mul(sz0, Mathx.Sub(Mathx.Step(Vector4.zero, gx0), 0.5f));
gy0 -= Mathx.Mul(sz0, Mathx.Sub(Mathx.Step(Vector4.zero, gy0), 0.5f));
Vector4 gx1 = ixy1 * (1.0f / 7.0f);
Vector4 gy1 = Mathx.Sub(Mathx.Frac(Mathx.Floor(gx1) * (1.0f / 7.0f)), 0.5f);
gx1 = Mathx.Frac(gx1);
Vector4 gz1 = Vector4.one * 0.5f - Mathx.Abs(gx1) - Mathx.Abs(gy1);
Vector4 sz1 = Mathx.Step(gz1, Vector4.zero);
gx1 -= Mathx.Mul(sz1, Mathx.Sub(Mathx.Step(Vector4.zero, gx1), 0.5f));
gy1 -= Mathx.Mul(sz1, Mathx.Sub(Mathx.Step(Vector4.zero, gy1), 0.5f));
Vector3 g000 = new Vector3(gx0.x, gy0.x, gz0.x);
Vector3 g100 = new Vector3(gx0.y, gy0.y, gz0.y);
Vector3 g010 = new Vector3(gx0.z, gy0.z, gz0.z);
Vector3 g110 = new Vector3(gx0.w, gy0.w, gz0.w);
Vector3 g001 = new Vector3(gx1.x, gy1.x, gz1.x);
Vector3 g101 = new Vector3(gx1.y, gy1.y, gz1.y);
Vector3 g011 = new Vector3(gx1.z, gy1.z, gz1.z);
Vector3 g111 = new Vector3(gx1.w, gy1.w, gz1.w);
Vector4 TaylorInvSqrt(Vector4 v)
{
return(Mathx.Sub(1.79284291400159f, Mathx.Mul(0.85373472095314f, v)));
}
Vector4 norm0 = TaylorInvSqrt(new Vector4(
Vector3.Dot(g000, g000),
Vector3.Dot(g010, g010),
Vector3.Dot(g100, g100),
Vector3.Dot(g110, g110)
));
g000 *= norm0.x;
g010 *= norm0.y;
g100 *= norm0.z;
g110 *= norm0.w;
Vector4 norm1 = TaylorInvSqrt(new Vector4(
Vector3.Dot(g001, g001),
Vector3.Dot(g011, g011),
Vector3.Dot(g101, g101),
Vector3.Dot(g111, g111)
));
g001 *= norm1.x;
g011 *= norm1.y;
g101 *= norm1.z;
g111 *= norm1.w;
float n000 = Vector3.Dot(g000, Pf0);
float n100 = Vector3.Dot(g100, new Vector3(Pf1.x, Pf0.y, Pf0.z));
float n010 = Vector3.Dot(g010, new Vector3(Pf0.x, Pf1.y, Pf0.z));
float n110 = Vector3.Dot(g110, new Vector3(Pf1.x, Pf1.y, Pf0.z));
float n001 = Vector3.Dot(g001, new Vector3(Pf0.x, Pf0.y, Pf1.z));
float n101 = Vector3.Dot(g101, new Vector3(Pf1.x, Pf0.y, Pf1.z));
float n011 = Vector3.Dot(g011, new Vector3(Pf0.x, Pf1.y, Pf1.z));
float n111 = Vector3.Dot(g111, Pf1);
Vector3 fade_xyz = Mathx.SmootherStep(Pf0);
Vector4 n_z = Vector4.Lerp(new Vector4(n000, n100, n010, n110), new Vector4(n001, n101, n011, n111), fade_xyz.z);
Vector2 n_yz = Vector2.Lerp(new Vector2(n_z.x, n_z.y), new Vector2(n_z.z, n_z.w), fade_xyz.y);
float n_xyz = Mathf.Lerp(n_yz.x, n_yz.y, fade_xyz.x);
return(2.2f * n_xyz);
}
public static Vector2 Centroid(params Vector2[] vs)
{
return(Mathx.Average(vs));
}
public void Include(Vector3Int otherMin, Vector3Int otherMax)
{
min = Mathx.Min(min, otherMin);
max = Mathx.Max(max, otherMax);
}
public bool IsValid()
{
return(!Mathx.IsZero(x) || !Mathx.IsZero(y));
}
public bool IsValid()
{
return(!Mathx.IsZero(a) && !Mathx.IsZero(b));
}
public static Vector3 ToNormal(Color c)
{
return((Mathx.Sub(Mathx.Mul(ToVector3(c), 2), 1)).XZY());
}
