902 lines
47 KiB
C#
902 lines
47 KiB
C#
using System.Runtime.CompilerServices;
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using static Unity.Mathematics.math;
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namespace Unity.Mathematics
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{
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public partial struct float2x2
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{
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/// <summary>Returns a float2x2 matrix representing a counter-clockwise rotation of angle degrees.</summary>
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public static float2x2 Rotate(float angle)
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{
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float s, c;
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sincos(angle, out s, out c);
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return float2x2(c, -s,
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s, c);
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}
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/// <summary>Returns a float2x2 matrix representing a uniform scaling of both axes by s.</summary>
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public static float2x2 Scale(float s)
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{
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return float2x2(s, 0.0f,
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0.0f, s);
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}
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/// <summary>Returns a float2x2 matrix representing a non-uniform axis scaling by x and y.</summary>
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public static float2x2 Scale(float x, float y)
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{
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return float2x2(x, 0.0f,
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0.0f, y);
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}
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/// <summary>Returns a float2x2 matrix representing a non-uniform axis scaling by the components of the float2 vector v.</summary>
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public static float2x2 Scale(float2 v)
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{
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return Scale(v.x, v.y);
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}
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}
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public partial struct float3x3
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{
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/// <summary>Constructs a float3x3 matrix from a unit quaternion.</summary>
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public float3x3(quaternion q)
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{
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float4 v = q.value;
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float4 v2 = v + v;
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uint3 npn = uint3(0x80000000, 0x00000000, 0x80000000);
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uint3 nnp = uint3(0x80000000, 0x80000000, 0x00000000);
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uint3 pnn = uint3(0x00000000, 0x80000000, 0x80000000);
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c0 = v2.y * asfloat(asuint(v.yxw) ^ npn) - v2.z * asfloat(asuint(v.zwx) ^ pnn) + float3(1, 0, 0);
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c1 = v2.z * asfloat(asuint(v.wzy) ^ nnp) - v2.x * asfloat(asuint(v.yxw) ^ npn) + float3(0, 1, 0);
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c2 = v2.x * asfloat(asuint(v.zwx) ^ pnn) - v2.y * asfloat(asuint(v.wzy) ^ nnp) + float3(0, 0, 1);
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}
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/// <summary>
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/// Returns a float3x3 matrix representing a rotation around a unit axis by an angle in radians.
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/// The rotation direction is clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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public static float3x3 AxisAngle(float3 axis, float angle)
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{
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float sina, cosa;
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math.sincos(angle, out sina, out cosa);
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float3 u = axis;
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float3 u_yzx = u.yzx;
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float3 u_zxy = u.zxy;
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float3 u_inv_cosa = u - u * cosa; // u * (1.0f - cosa);
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float4 t = float4(u * sina, cosa);
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uint3 ppn = uint3(0x00000000, 0x00000000, 0x80000000);
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uint3 npp = uint3(0x80000000, 0x00000000, 0x00000000);
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uint3 pnp = uint3(0x00000000, 0x80000000, 0x00000000);
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return float3x3(
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u.x * u_inv_cosa + asfloat(asuint(t.wzy) ^ ppn),
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u.y * u_inv_cosa + asfloat(asuint(t.zwx) ^ npp),
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u.z * u_inv_cosa + asfloat(asuint(t.yxw) ^ pnp)
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);
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/*
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return float3x3(
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cosa + u.x * u.x * (1.0f - cosa), u.y * u.x * (1.0f - cosa) - u.z * sina, u.z * u.x * (1.0f - cosa) + u.y * sina,
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u.x * u.y * (1.0f - cosa) + u.z * sina, cosa + u.y * u.y * (1.0f - cosa), u.y * u.z * (1.0f - cosa) - u.x * sina,
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u.x * u.z * (1.0f - cosa) - u.y * sina, u.y * u.z * (1.0f - cosa) + u.x * sina, cosa + u.z * u.z * (1.0f - cosa)
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);
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*/
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the x-axis, then the y-axis and finally the z-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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public static float3x3 EulerXYZ(float3 xyz)
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{
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// return mul(rotateZ(xyz.z), mul(rotateY(xyz.y), rotateX(xyz.x)));
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float3 s, c;
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sincos(xyz, out s, out c);
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return float3x3(
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c.y * c.z, c.z * s.x * s.y - c.x * s.z, c.x * c.z * s.y + s.x * s.z,
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c.y * s.z, c.x * c.z + s.x * s.y * s.z, c.x * s.y * s.z - c.z * s.x,
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-s.y, c.y * s.x, c.x * c.y
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);
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the x-axis, then the z-axis and finally the y-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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public static float3x3 EulerXZY(float3 xyz)
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{
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// return mul(rotateY(xyz.y), mul(rotateZ(xyz.z), rotateX(xyz.x))); }
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float3 s, c;
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sincos(xyz, out s, out c);
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return float3x3(
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c.y * c.z, s.x * s.y - c.x * c.y * s.z, c.x * s.y + c.y * s.x * s.z,
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s.z, c.x * c.z, -c.z * s.x,
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-c.z * s.y, c.y * s.x + c.x * s.y * s.z, c.x * c.y - s.x * s.y * s.z
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);
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the y-axis, then the x-axis and finally the z-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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public static float3x3 EulerYXZ(float3 xyz)
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{
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// return mul(rotateZ(xyz.z), mul(rotateX(xyz.x), rotateY(xyz.y)));
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float3 s, c;
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sincos(xyz, out s, out c);
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return float3x3(
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c.y * c.z - s.x * s.y * s.z, -c.x * s.z, c.z * s.y + c.y * s.x * s.z,
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c.z * s.x * s.y + c.y * s.z, c.x * c.z, s.y * s.z - c.y * c.z * s.x,
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-c.x * s.y, s.x, c.x * c.y
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);
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the y-axis, then the z-axis and finally the x-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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public static float3x3 EulerYZX(float3 xyz)
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{
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// return mul(rotateX(xyz.x), mul(rotateZ(xyz.z), rotateY(xyz.y)));
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float3 s, c;
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sincos(xyz, out s, out c);
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return float3x3(
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c.y * c.z, -s.z, c.z * s.y,
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s.x * s.y + c.x * c.y * s.z, c.x * c.z, c.x * s.y * s.z - c.y * s.x,
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c.y * s.x * s.z - c.x * s.y, c.z * s.x, c.x * c.y + s.x * s.y * s.z
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);
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the z-axis, then the x-axis and finally the y-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// This is the default order rotation order in Unity.
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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public static float3x3 EulerZXY(float3 xyz)
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{
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// return mul(rotateY(xyz.y), mul(rotateX(xyz.x), rotateZ(xyz.z)));
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float3 s, c;
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sincos(xyz, out s, out c);
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return float3x3(
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c.y * c.z + s.x * s.y * s.z, c.z * s.x * s.y - c.y * s.z, c.x * s.y,
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c.x * s.z, c.x * c.z, -s.x,
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c.y * s.x * s.z - c.z * s.y, c.y * c.z * s.x + s.y * s.z, c.x * c.y
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);
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the z-axis, then the y-axis and finally the x-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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public static float3x3 EulerZYX(float3 xyz)
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{
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// return mul(rotateX(xyz.x), mul(rotateY(xyz.y), rotateZ(xyz.z)));
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float3 s, c;
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sincos(xyz, out s, out c);
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return float3x3(
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c.y * c.z, -c.y * s.z, s.y,
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c.z * s.x * s.y + c.x * s.z, c.x * c.z - s.x * s.y * s.z, -c.y * s.x,
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s.x * s.z - c.x * c.z * s.y, c.z * s.x + c.x * s.y * s.z, c.x * c.y
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);
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the x-axis, then the y-axis and finally the z-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 EulerXYZ(float x, float y, float z) { return EulerXYZ(float3(x, y, z)); }
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the x-axis, then the z-axis and finally the y-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 EulerXZY(float x, float y, float z) { return EulerXZY(float3(x, y, z)); }
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the y-axis, then the x-axis and finally the z-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 EulerYXZ(float x, float y, float z) { return EulerYXZ(float3(x, y, z)); }
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the y-axis, then the z-axis and finally the x-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 EulerYZX(float x, float y, float z) { return EulerYZX(float3(x, y, z)); }
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the z-axis, then the x-axis and finally the y-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// This is the default order rotation order in Unity.
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 EulerZXY(float x, float y, float z) { return EulerZXY(float3(x, y, z)); }
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing a rotation around the z-axis, then the y-axis and finally the x-axis.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 EulerZYX(float x, float y, float z) { return EulerZYX(float3(x, y, z)); }
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing 3 rotations around the principal axes in a given order.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// When the rotation order is known at compile time, it is recommended for performance reasons to use specific
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/// Euler rotation constructors such as EulerZXY(...).
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/// </summary>
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/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
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/// <param name="order">The order in which the rotations are applied.</param>
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public static float3x3 Euler(float3 xyz, RotationOrder order = RotationOrder.Default)
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{
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switch (order)
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{
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case RotationOrder.XYZ:
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return EulerXYZ(xyz);
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case RotationOrder.XZY:
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return EulerXZY(xyz);
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case RotationOrder.YXZ:
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return EulerYXZ(xyz);
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case RotationOrder.YZX:
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return EulerYZX(xyz);
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case RotationOrder.ZXY:
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return EulerZXY(xyz);
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case RotationOrder.ZYX:
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return EulerZYX(xyz);
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default:
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return float3x3.identity;
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}
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}
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/// <summary>
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/// Returns a float3x3 rotation matrix constructed by first performing 3 rotations around the principal axes in a given order.
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/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
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/// When the rotation order is known at compile time, it is recommended for performance reasons to use specific
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/// Euler rotation constructors such as EulerZXY(...).
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/// </summary>
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/// <param name="x">The rotation angle around the x-axis in radians.</param>
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/// <param name="y">The rotation angle around the y-axis in radians.</param>
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/// <param name="z">The rotation angle around the z-axis in radians.</param>
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/// <param name="order">The order in which the rotations are applied.</param>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 Euler(float x, float y, float z, RotationOrder order = RotationOrder.Default)
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{
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return Euler(float3(x, y, z), order);
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}
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/// <summary>Returns a float4x4 matrix that rotates around the x-axis by a given number of radians.</summary>
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/// <param name="angle">The clockwise rotation angle when looking along the x-axis towards the origin in radians.</param>
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public static float3x3 RotateX(float angle)
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{
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// {{1, 0, 0}, {0, c_0, -s_0}, {0, s_0, c_0}}
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float s, c;
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sincos(angle, out s, out c);
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return float3x3(1.0f, 0.0f, 0.0f,
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0.0f, c, -s,
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0.0f, s, c);
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}
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/// <summary>Returns a float4x4 matrix that rotates around the y-axis by a given number of radians.</summary>
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/// <param name="angle">The clockwise rotation angle when looking along the y-axis towards the origin in radians.</param>
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public static float3x3 RotateY(float angle)
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{
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// {{c_1, 0, s_1}, {0, 1, 0}, {-s_1, 0, c_1}}
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float s, c;
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sincos(angle, out s, out c);
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return float3x3(c, 0.0f, s,
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0.0f, 1.0f, 0.0f,
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-s, 0.0f, c);
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}
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/// <summary>Returns a float4x4 matrix that rotates around the z-axis by a given number of radians.</summary>
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/// <param name="angle">The clockwise rotation angle when looking along the z-axis towards the origin in radians.</param>
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public static float3x3 RotateZ(float angle)
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{
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// {{c_2, -s_2, 0}, {s_2, c_2, 0}, {0, 0, 1}}
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float s, c;
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sincos(angle, out s, out c);
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return float3x3(c, -s, 0.0f,
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s, c, 0.0f,
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0.0f, 0.0f, 1.0f);
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}
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//<summary>Returns a float3x3 matrix representing a uniform scaling of all axes by s.</summary>
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public static float3x3 Scale(float s)
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{
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return float3x3(s, 0.0f, 0.0f,
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0.0f, s, 0.0f,
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0.0f, 0.0f, s);
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}
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/// <summary>Returns a float3x3 matrix representing a non-uniform axis scaling by x, y and z.</summary>
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public static float3x3 Scale(float x, float y, float z)
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{
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return float3x3(x, 0.0f, 0.0f,
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0.0f, y, 0.0f,
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0.0f, 0.0f, z);
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}
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/// <summary>Returns a float3x3 matrix representing a non-uniform axis scaling by the components of the float3 vector v.</summary>
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public static float3x3 Scale(float3 v)
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{
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return Scale(v.x, v.y, v.z);
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}
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/// <summary>
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/// Returns a float3x3 view rotation matrix given a unit length forward vector and a unit length up vector.
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/// The two input vectors are assumed to be unit length and not collinear.
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/// If these assumptions are not met use float3x3.LookRotationSafe instead.
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/// </summary>
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public static float3x3 LookRotation(float3 forward, float3 up)
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{
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float3 t = normalize(cross(up, forward));
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return float3x3(t, cross(forward, t), forward);
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}
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/// <summary>
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/// Returns a float3x3 view rotation matrix given a forward vector and an up vector.
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/// The two input vectors are not assumed to be unit length.
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/// If the magnitude of either of the vectors is so extreme that the calculation cannot be carried out reliably or the vectors are collinear,
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/// the identity will be returned instead.
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/// </summary>
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public static float3x3 LookRotationSafe(float3 forward, float3 up)
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{
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float forwardLengthSq = dot(forward, forward);
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float upLengthSq = dot(up, up);
|
|
|
|
forward *= rsqrt(forwardLengthSq);
|
|
up *= rsqrt(upLengthSq);
|
|
|
|
float3 t = cross(up, forward);
|
|
float tLengthSq = dot(t, t);
|
|
t *= rsqrt(tLengthSq);
|
|
|
|
float mn = min(min(forwardLengthSq, upLengthSq), tLengthSq);
|
|
float mx = max(max(forwardLengthSq, upLengthSq), tLengthSq);
|
|
|
|
bool accept = mn > 1e-35f && mx < 1e35f && isfinite(forwardLengthSq) && isfinite(upLengthSq) && isfinite(tLengthSq);
|
|
return float3x3(
|
|
select(float3(1,0,0), t, accept),
|
|
select(float3(0,1,0), cross(forward, t), accept),
|
|
select(float3(0,0,1), forward, accept));
|
|
}
|
|
}
|
|
|
|
public partial struct float4x4
|
|
{
|
|
/// <summary>Constructs a float4x4 from a float3x3 rotation matrix and a float3 translation vector.</summary>
|
|
public float4x4(float3x3 rotation, float3 translation)
|
|
{
|
|
c0 = float4(rotation.c0, 0.0f);
|
|
c1 = float4(rotation.c1, 0.0f);
|
|
c2 = float4(rotation.c2, 0.0f);
|
|
c3 = float4(translation, 1.0f);
|
|
}
|
|
|
|
/// <summary>Constructs a float4x4 from a quaternion and a float3 translation vector.</summary>
|
|
public float4x4(quaternion rotation, float3 translation)
|
|
{
|
|
float3x3 rot = float3x3(rotation);
|
|
c0 = float4(rot.c0, 0.0f);
|
|
c1 = float4(rot.c1, 0.0f);
|
|
c2 = float4(rot.c2, 0.0f);
|
|
c3 = float4(translation, 1.0f);
|
|
}
|
|
|
|
/// <summary>Constructs a float4x4 from a RigidTransform.</summary>
|
|
public float4x4(RigidTransform transform)
|
|
{
|
|
float3x3 rot = float3x3(transform.rot);
|
|
c0 = float4(rot.c0, 0.0f);
|
|
c1 = float4(rot.c1, 0.0f);
|
|
c2 = float4(rot.c2, 0.0f);
|
|
c3 = float4(transform.pos, 1.0f);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 matrix representing a rotation around a unit axis by an angle in radians.
|
|
/// The rotation direction is clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
public static float4x4 AxisAngle(float3 axis, float angle)
|
|
{
|
|
float sina, cosa;
|
|
math.sincos(angle, out sina, out cosa);
|
|
|
|
float4 u = float4(axis, 0.0f);
|
|
float4 u_yzx = u.yzxx;
|
|
float4 u_zxy = u.zxyx;
|
|
float4 u_inv_cosa = u - u * cosa; // u * (1.0f - cosa);
|
|
float4 t = float4(u.xyz * sina, cosa);
|
|
|
|
uint4 ppnp = uint4(0x00000000, 0x00000000, 0x80000000, 0x00000000);
|
|
uint4 nppp = uint4(0x80000000, 0x00000000, 0x00000000, 0x00000000);
|
|
uint4 pnpp = uint4(0x00000000, 0x80000000, 0x00000000, 0x00000000);
|
|
uint4 mask = uint4(0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000);
|
|
|
|
return float4x4(
|
|
u.x * u_inv_cosa + asfloat((asuint(t.wzyx) ^ ppnp) & mask),
|
|
u.y * u_inv_cosa + asfloat((asuint(t.zwxx) ^ nppp) & mask),
|
|
u.z * u_inv_cosa + asfloat((asuint(t.yxwx) ^ pnpp) & mask),
|
|
float4(0.0f, 0.0f, 0.0f, 1.0f)
|
|
);
|
|
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the x-axis, then the y-axis and finally the z-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
|
|
public static float4x4 EulerXYZ(float3 xyz)
|
|
{
|
|
// return mul(rotateZ(xyz.z), mul(rotateY(xyz.y), rotateX(xyz.x)));
|
|
float3 s, c;
|
|
sincos(xyz, out s, out c);
|
|
return float4x4(
|
|
c.y * c.z, c.z * s.x * s.y - c.x * s.z, c.x * c.z * s.y + s.x * s.z, 0.0f,
|
|
c.y * s.z, c.x * c.z + s.x * s.y * s.z, c.x * s.y * s.z - c.z * s.x, 0.0f,
|
|
-s.y, c.y * s.x, c.x * c.y, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the x-axis, then the z-axis and finally the y-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
|
|
public static float4x4 EulerXZY(float3 xyz)
|
|
{
|
|
// return mul(rotateY(xyz.y), mul(rotateZ(xyz.z), rotateX(xyz.x))); }
|
|
float3 s, c;
|
|
sincos(xyz, out s, out c);
|
|
return float4x4(
|
|
c.y * c.z, s.x * s.y - c.x * c.y * s.z, c.x * s.y + c.y * s.x * s.z, 0.0f,
|
|
s.z, c.x * c.z, -c.z * s.x, 0.0f,
|
|
-c.z * s.y, c.y * s.x + c.x * s.y * s.z, c.x * c.y - s.x * s.y * s.z, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the y-axis, then the x-axis and finally the z-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
|
|
public static float4x4 EulerYXZ(float3 xyz)
|
|
{
|
|
// return mul(rotateZ(xyz.z), mul(rotateX(xyz.x), rotateY(xyz.y)));
|
|
float3 s, c;
|
|
sincos(xyz, out s, out c);
|
|
return float4x4(
|
|
c.y * c.z - s.x * s.y * s.z, -c.x * s.z, c.z * s.y + c.y * s.x * s.z, 0.0f,
|
|
c.z * s.x * s.y + c.y * s.z, c.x * c.z, s.y * s.z - c.y * c.z * s.x, 0.0f,
|
|
-c.x * s.y, s.x, c.x * c.y, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the y-axis, then the z-axis and finally the x-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
|
|
public static float4x4 EulerYZX(float3 xyz)
|
|
{
|
|
// return mul(rotateX(xyz.x), mul(rotateZ(xyz.z), rotateY(xyz.y)));
|
|
float3 s, c;
|
|
sincos(xyz, out s, out c);
|
|
return float4x4(
|
|
c.y * c.z, -s.z, c.z * s.y, 0.0f,
|
|
s.x * s.y + c.x * c.y * s.z, c.x * c.z, c.x * s.y * s.z - c.y * s.x, 0.0f,
|
|
c.y * s.x * s.z - c.x * s.y, c.z * s.x, c.x * c.y + s.x * s.y * s.z, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the z-axis, then the x-axis and finally the y-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// This is the default order rotation order in Unity.
|
|
/// </summary>
|
|
/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
|
|
public static float4x4 EulerZXY(float3 xyz)
|
|
{
|
|
// return mul(rotateY(xyz.y), mul(rotateX(xyz.x), rotateZ(xyz.z)));
|
|
float3 s, c;
|
|
sincos(xyz, out s, out c);
|
|
return float4x4(
|
|
c.y * c.z + s.x * s.y * s.z, c.z * s.x * s.y - c.y * s.z, c.x * s.y, 0.0f,
|
|
c.x * s.z, c.x * c.z, -s.x, 0.0f,
|
|
c.y * s.x * s.z - c.z * s.y, c.y * c.z * s.x + s.y * s.z, c.x * c.y, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the z-axis, then the y-axis and finally the x-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="xyz">A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.</param>
|
|
public static float4x4 EulerZYX(float3 xyz)
|
|
{
|
|
// return mul(rotateX(xyz.x), mul(rotateY(xyz.y), rotateZ(xyz.z)));
|
|
float3 s, c;
|
|
sincos(xyz, out s, out c);
|
|
return float4x4(
|
|
c.y * c.z, -c.y * s.z, s.y, 0.0f,
|
|
c.z * s.x * s.y + c.x * s.z, c.x * c.z - s.x * s.y * s.z, -c.y * s.x, 0.0f,
|
|
s.x * s.z - c.x * c.z * s.y, c.z * s.x + c.x * s.y * s.z, c.x * c.y, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the x-axis, then the y-axis and finally the z-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 EulerXYZ(float x, float y, float z) { return EulerXYZ(float3(x, y, z)); }
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the x-axis, then the z-axis and finally the y-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 EulerXZY(float x, float y, float z) { return EulerXZY(float3(x, y, z)); }
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the y-axis, then the x-axis and finally the z-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 EulerYXZ(float x, float y, float z) { return EulerYXZ(float3(x, y, z)); }
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the y-axis, then the z-axis and finally the x-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 EulerYZX(float x, float y, float z) { return EulerYZX(float3(x, y, z)); }
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the z-axis, then the x-axis and finally the y-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// This is the default order rotation order in Unity.
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 EulerZXY(float x, float y, float z) { return EulerZXY(float3(x, y, z)); }
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing a rotation around the z-axis, then the y-axis and finally the x-axis.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 EulerZYX(float x, float y, float z) { return EulerZYX(float3(x, y, z)); }
|
|
|
|
public static float4x4 Euler(float3 xyz, RotationOrder order = RotationOrder.Default)
|
|
{
|
|
switch (order)
|
|
{
|
|
case RotationOrder.XYZ:
|
|
return EulerXYZ(xyz);
|
|
case RotationOrder.XZY:
|
|
return EulerXZY(xyz);
|
|
case RotationOrder.YXZ:
|
|
return EulerYXZ(xyz);
|
|
case RotationOrder.YZX:
|
|
return EulerYZX(xyz);
|
|
case RotationOrder.ZXY:
|
|
return EulerZXY(xyz);
|
|
case RotationOrder.ZYX:
|
|
return EulerZYX(xyz);
|
|
default:
|
|
return float4x4.identity;
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 rotation matrix constructed by first performing 3 rotations around the principal axes in a given order.
|
|
/// All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.
|
|
/// When the rotation order is known at compile time, it is recommended for performance reasons to use specific
|
|
/// Euler rotation constructors such as EulerZXY(...).
|
|
/// </summary>
|
|
/// <param name="x">The rotation angle around the x-axis in radians.</param>
|
|
/// <param name="y">The rotation angle around the y-axis in radians.</param>
|
|
/// <param name="z">The rotation angle around the z-axis in radians.</param>
|
|
/// <param name="order">The order in which the rotations are applied.</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4x4 Euler(float x, float y, float z, RotationOrder order = RotationOrder.Default)
|
|
{
|
|
return Euler(float3(x, y, z), order);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 matrix that rotates around the x-axis by a given number of radians.</summary>
|
|
/// <param name="angle">The clockwise rotation angle when looking along the x-axis towards the origin in radians.</param>
|
|
public static float4x4 RotateX(float angle)
|
|
{
|
|
// {{1, 0, 0}, {0, c_0, -s_0}, {0, s_0, c_0}}
|
|
float s, c;
|
|
sincos(angle, out s, out c);
|
|
return float4x4(1.0f, 0.0f, 0.0f, 0.0f,
|
|
0.0f, c, -s, 0.0f,
|
|
0.0f, s, c, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f);
|
|
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 matrix that rotates around the y-axis by a given number of radians.</summary>
|
|
/// <param name="angle">The clockwise rotation angle when looking along the y-axis towards the origin in radians.</param>
|
|
public static float4x4 RotateY(float angle)
|
|
{
|
|
// {{c_1, 0, s_1}, {0, 1, 0}, {-s_1, 0, c_1}}
|
|
float s, c;
|
|
sincos(angle, out s, out c);
|
|
return float4x4(c, 0.0f, s, 0.0f,
|
|
0.0f, 1.0f, 0.0f, 0.0f,
|
|
-s, 0.0f, c, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f);
|
|
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 matrix that rotates around the z-axis by a given number of radians.</summary>
|
|
/// <param name="angle">The clockwise rotation angle when looking along the z-axis towards the origin in radians.</param>
|
|
public static float4x4 RotateZ(float angle)
|
|
{
|
|
// {{c_2, -s_2, 0}, {s_2, c_2, 0}, {0, 0, 1}}
|
|
float s, c;
|
|
sincos(angle, out s, out c);
|
|
return float4x4(c, -s, 0.0f, 0.0f,
|
|
s, c, 0.0f, 0.0f,
|
|
0.0f, 0.0f, 1.0f, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f);
|
|
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 scale matrix given 3 axis scales.</summary>
|
|
public static float4x4 Scale(float s)
|
|
{
|
|
return float4x4(s, 0.0f, 0.0f, 0.0f,
|
|
0.0f, s, 0.0f, 0.0f,
|
|
0.0f, 0.0f, s, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 scale matrix given a float3 vector containing the 3 axis scales.</summary>
|
|
public static float4x4 Scale(float x, float y, float z)
|
|
{
|
|
return float4x4(x, 0.0f, 0.0f, 0.0f,
|
|
0.0f, y, 0.0f, 0.0f,
|
|
0.0f, 0.0f, z, 0.0f,
|
|
0.0f, 0.0f, 0.0f, 1.0f);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 scale matrix given a float3 vector containing the 3 axis scales.</summary>
|
|
public static float4x4 Scale(float3 scales)
|
|
{
|
|
return Scale(scales.x, scales.y, scales.z);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 translation matrix given a float3 translation vector.</summary>
|
|
public static float4x4 Translate(float3 vector)
|
|
{
|
|
return float4x4(float4(1.0f, 0.0f, 0.0f, 0.0f),
|
|
float4(0.0f, 1.0f, 0.0f, 0.0f),
|
|
float4(0.0f, 0.0f, 1.0f, 0.0f),
|
|
float4(vector.x, vector.y, vector.z, 1.0f));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 view matrix given an eye position, a target point and a unit length up vector.
|
|
/// The up vector is assumed to be unit length, the eye and target points are assumed to be distinct and
|
|
/// the vector between them is assumes to be collinear with the up vector.
|
|
/// If these assumptions are not met use float4x4.LookRotationSafe instead.
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|
/// </summary>
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public static float4x4 LookAt(float3 eye, float3 target, float3 up)
|
|
{
|
|
float3x3 rot = float3x3.LookRotation(normalize(target - eye), up);
|
|
|
|
float4x4 matrix;
|
|
matrix.c0 = float4(rot.c0, 0.0F);
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matrix.c1 = float4(rot.c1, 0.0F);
|
|
matrix.c2 = float4(rot.c2, 0.0F);
|
|
matrix.c3 = float4(eye, 1.0F);
|
|
return matrix;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 centered orthographic projection matrix.
|
|
/// </summary>
|
|
/// <param name="width">The width of the view volume.</param>
|
|
/// <param name="height">The height of the view volume.</param>
|
|
/// <param name="near">The distance to the near plane.</param>
|
|
/// <param name="far">The distance to the far plane.</param>
|
|
public static float4x4 Ortho(float width, float height, float near, float far)
|
|
{
|
|
float rcpdx = 1.0f / width;
|
|
float rcpdy = 1.0f / height;
|
|
float rcpdz = 1.0f / (far - near);
|
|
|
|
return float4x4(
|
|
2.0f * rcpdx, 0.0f, 0.0f, 0.0f,
|
|
0.0f, 2.0f * rcpdy, 0.0f, 0.0f,
|
|
0.0f, 0.0f, -2.0f * rcpdz, -(far + near) * rcpdz,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 off-center orthographic projection matrix.
|
|
/// </summary>
|
|
/// <param name="left">The minimum x-coordinate of the view volume.</param>
|
|
/// <param name="right">The maximum x-coordinate of the view volume.</param>
|
|
/// <param name="bottom">The minimum y-coordinate of the view volume.</param>
|
|
/// <param name="top">The minimum y-coordinate of the view volume.</param>
|
|
/// <param name="near">The distance to the near plane.</param>
|
|
/// <param name="far">The distance to the far plane.</param>
|
|
public static float4x4 OrthoOffCenter(float left, float right, float bottom, float top, float near, float far)
|
|
{
|
|
float rcpdx = 1.0f / (right - left);
|
|
float rcpdy = 1.0f / (top - bottom);
|
|
float rcpdz = 1.0f / (far - near);
|
|
|
|
return float4x4(
|
|
2.0f * rcpdx, 0.0f, 0.0f, -(right + left) * rcpdx,
|
|
0.0f, 2.0f * rcpdy, 0.0f, -(top + bottom) * rcpdy,
|
|
0.0f, 0.0f, -2.0f * rcpdz, -(far + near) * rcpdz,
|
|
0.0f, 0.0f, 0.0f, 1.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 perspective projection matrix based on field of view.
|
|
/// </summary>
|
|
/// <param name="verticalFov">Vertical Field of view in radians.</param>
|
|
/// <param name="aspect">X:Y aspect ratio.</param>
|
|
/// <param name="near">Distance to near plane. Must be greater than zero.</param>
|
|
/// <param name="far">Distance to far plane. Must be greater than zero.</param>
|
|
public static float4x4 PerspectiveFov(float verticalFov, float aspect, float near, float far)
|
|
{
|
|
float cotangent = 1.0f / tan(verticalFov * 0.5f);
|
|
float rcpdz = 1.0f / (near - far);
|
|
|
|
return float4x4(
|
|
cotangent / aspect, 0.0f, 0.0f, 0.0f,
|
|
0.0f, cotangent, 0.0f, 0.0f,
|
|
0.0f, 0.0f, (far + near) * rcpdz, 2.0f * near * far * rcpdz,
|
|
0.0f, 0.0f, -1.0f, 0.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 off-center perspective projection matrix.
|
|
/// </summary>
|
|
/// <param name="left">The x-coordinate of the left side of the clipping frustum at the near plane.</param>
|
|
/// <param name="right">The x-coordinate of the right side of the clipping frustum at the near plane.</param>
|
|
/// <param name="bottom">The y-coordinate of the bottom side of the clipping frustum at the near plane.</param>
|
|
/// <param name="top">The y-coordinate of the top side of the clipping frustum at the near plane.</param>
|
|
/// <param name="near">Distance to the near plane. Must be greater than zero.</param>
|
|
/// <param name="far">Distance to the far plane. Must be greater than zero.</param>
|
|
public static float4x4 PerspectiveOffCenter(float left, float right, float bottom, float top, float near, float far)
|
|
{
|
|
float rcpdz = 1.0f / (near - far);
|
|
float rcpWidth = 1.0f / (right - left);
|
|
float rcpHeight = 1.0f / (top - bottom);
|
|
|
|
return float4x4(
|
|
2.0f * near * rcpWidth, 0.0f, (left + right) * rcpWidth, 0.0f,
|
|
0.0f, 2.0f * near * rcpHeight, (bottom + top) * rcpHeight, 0.0f,
|
|
0.0f, 0.0f, (far + near) * rcpdz, 2.0f * near * far * rcpdz,
|
|
0.0f, 0.0f, -1.0f, 0.0f
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a float4x4 matrix representing a combined scale-, rotation- and translation transform.
|
|
/// Equivalent to mul(translationTransform, mul(rotationTransform, scaleTransform)).
|
|
/// </summary>
|
|
public static float4x4 TRS(float3 translation, quaternion rotation, float3 scale)
|
|
{
|
|
float3x3 r = float3x3(rotation);
|
|
return float4x4( float4(r.c0 * scale.x, 0.0f),
|
|
float4(r.c1 * scale.y, 0.0f),
|
|
float4(r.c2 * scale.z, 0.0f),
|
|
float4(translation, 1.0f));
|
|
}
|
|
}
|
|
|
|
partial class math
|
|
{
|
|
/// <summary>Returns a float3x3 matrix constructed from a quaternion.</summary>
|
|
public static float3x3 float3x3(quaternion rotation)
|
|
{
|
|
return new float3x3(rotation);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 constructed from a float3x3 rotation matrix and a float3 translation vector.</summary>
|
|
public static float4x4 float4x4(float3x3 rotation, float3 translation)
|
|
{
|
|
return new float4x4(rotation, translation);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 constructed from a quaternion and a float3 translation vector.</summary>
|
|
public static float4x4 float4x4(quaternion rotation, float3 translation)
|
|
{
|
|
return new float4x4(rotation, translation);
|
|
}
|
|
|
|
/// <summary>Returns a float4x4 constructed from a RigidTransform.</summary>
|
|
public static float4x4 float4x4(RigidTransform transform)
|
|
{
|
|
return new float4x4(transform);
|
|
}
|
|
|
|
/// <summary>Returns an orthonormalized version of a float3x3 matrix.</summary>
|
|
public static float3x3 orthonormalize(float3x3 i)
|
|
{
|
|
float3x3 o;
|
|
|
|
float3 u = i.c0;
|
|
float3 v = i.c1 - i.c0 * math.dot(i.c1, i.c0);
|
|
|
|
float lenU = math.length(u);
|
|
float lenV = math.length(v);
|
|
|
|
bool c = lenU > 1e-30f && lenV > 1e-30f;
|
|
|
|
o.c0 = math.select(float3(1, 0, 0), u / lenU, c);
|
|
o.c1 = math.select(float3(0, 1, 0), v / lenV, c);
|
|
o.c2 = math.cross(o.c0, o.c1);
|
|
|
|
return o;
|
|
}
|
|
}
|
|
}
|