public void TestAbs1()
{
var expr = MathS.Abs(x) + 4;
var func = expr.Compile(x);
Assert.Equal(4, func.Call(0));
}
public void TestAbs3()
{
var expr = MathS.Abs(x) + 4;
var func = expr.Compile(x);
Assert.Equal(9, func.Call(new Complex(3, 4)));
}
public Vector3 ToVector3()
{
if (MathS.Abs(w) <= Threshold)
{
return(new Vector3(x, y, z));
}
else
{
return(new Vector3(x / w, y / w, z / w));
}
}
private IVertexOutputData[] ClipPolygon(IVertexOutputData[] polygon)
{
for (int planeIndex = 0; planeIndex < 6; planeIndex++)
{
List <IVertexOutputData> vdatas = new List <IVertexOutputData>();
int vi = planeIndex / 2;
int sign = planeIndex % 2 == 0 ? 1 : -1;
for (int pointIndex = 0; pointIndex < polygon.Length; pointIndex++)
{
int index0 = pointIndex;
int index1 = pointIndex == polygon.Length - 1 ? 0 : pointIndex + 1;
IVertexOutputData v0 = polygon[index0];
IVertexOutputData v1 = polygon[index1];
Vector4 p0 = v0.clip;
Vector4 p1 = v1.clip;
Vector3 n0 = v0.viewNormal;
Vector3 n1 = v1.viewNormal;
float d0 = (p0[vi] + p0.w * sign) * p0.w;
float d1 = (p1[vi] + p1.w * sign) * p1.w;
float ds = d0 * d1;
if (ds < 0)
{
// 边与裁剪面相交
float u = d0 / (d0 - d1);
Vector4 p = p0 + (p1 - p0) * u;
Vector3 n = n0 + (n1 - n0) * u;
if (sign * d0 > 0)
{
vdatas.Add(v0);
}
IVertexOutputData data = new VertexOutputData();
data.clip = p;
data.viewNormal = n;
vdatas.Add(data);
}
else if (MathS.Abs(d0) < Threshold)
{
// p0点在裁剪面上
vdatas.Add(v0);
}
else if (sign * d0 > 0 && sign * d1 >= 0)
{
// 边完全位于裁剪面之内
vdatas.Add(v0);
}
}
polygon = vdatas.ToArray();
}
return(polygon);
}
public IVertexOutputData Triangle(IVertexOutputData[] clips, Vector2[] screens, int[] pixel)
{
Vector2 center = new Vector2(pixel[0], pixel[1]);
float a = MathS.Abs(Vector2.Cross(screens[1] - screens[0], screens[2] - screens[0]) * 0.5f);
// 重心法求插值系数
float a0 = MathS.Abs(Vector2.Cross(screens[1] - screens[0], center - screens[0]) * 0.5f) / a;
float a1 = MathS.Abs(Vector2.Cross(screens[2] - screens[1], center - screens[1]) * 0.5f) / a;
float a2 = MathS.Abs(Vector2.Cross(screens[0] - screens[2], center - screens[2]) * 0.5f) / a;
// 插值
IVertexOutputData lerp = new VertexOutputData();
lerp.clip = a0 * clips[0].clip + a1 * clips[1].clip + a2 * clips[2].clip;
lerp.viewNormal = a0 * clips[0].viewNormal + a1 * clips[1].viewNormal + a2 * clips[2].viewNormal;
return(lerp);
}
public Vector3 Perpendicular()
{
float ax = MathS.Abs(x);
float ay = MathS.Abs(y);
float az = MathS.Abs(z);
if (ax < ay && ax < az)
{
return(new Vector3(0, -z, y));
}
else if (ay < ax && ay < az)
{
return(new Vector3(-z, 0, x));
}
else
{
return(new Vector3(-y, x, 0));
}
}
/// <summary>
/// 旋转单位向量From到另外一个单位向量To
/// </summary>
/// <param name="from">单位向量</param>
/// <param name="to">单位向量</param>
/// <returns>单位四元数</returns>
public static Quaternion FromTo(Vector3 from, Vector3 to)
{
Quaternion uq = Quaternion.identity;
float squar = 2 * (1 + Vector3.Dot(from, to));
if (MathS.Abs(squar) <= Threshold)
{
Vector3 perp = from.Perpendicular().normalized;
uq = new Quaternion(perp.x, perp.y, perp.z, 0);
}
else
{
float root = MathS.Sqrt(squar);
Vector3 imag = from.Cross(to) / root;
float real = root * 0.5f;
uq = new Quaternion(imag.x, imag.y, imag.z, real);
}
return(uq);
}
/// <summary>
/// 旋转轴和旋转角(单位四元数有效)
/// </summary>
/// <param name="angle"></param>
/// <param name="axisNormal"></param>
public void ToAngleAxis(out float angle, out Vector3 axisNormal)
{
Vector3 axis = new Vector3(
MathS.Abs(x) <= Threshold ? 0f : x,
MathS.Abs(y) <= Threshold ? 0f : y,
MathS.Abs(z) <= Threshold ? 0f : z
);
if (axis == Vector3.zero)
{
angle = 0;
axisNormal = Vector3.zero;
}
else
{
float length = axis.magnitude;
angle = MathS.Atan2(length, w) * 2 * MathS.RadToDeg;
axisNormal = axis / length;
}
}
/// <summary>
/// 欧拉角(单位四元数有效)
/// </summary>
/// <returns></returns>
public Vector3 ToEulers()
{
Vector3 euler = Vector3.zero;
Matrix m = ToMatrix();
if (MathS.Abs(m[1, 0]) <= Threshold &&
MathS.Abs(m[1, 1]) <= Threshold)
{
euler.x = m[1, 2] <= 0 ? 90 : -90;
euler.y = 0;
euler.z = MathS.Atan2(-m[0, 1], m[0, 0]) * MathS.RadToDeg;
}
else
{
euler.x = MathS.Asin(-m[1, 2]);
euler.y = MathS.Atan2(m[0, 2], m[2, 2]);
euler.z = MathS.Atan2(m[1, 0], m[1, 1]);
euler *= MathS.RadToDeg;
}
return(euler);
}
[Fact] public void Abs() => Test(@"\left|x\right|", MathS.Abs(x));
public float Distance(Vector3 point)
{
return(MathS.Abs(point.Dot(mNormal) - md));
}
