1023 lines
40 KiB
C#
1023 lines
40 KiB
C#
#if (OBI_BURST && OBI_MATHEMATICS && OBI_COLLECTIONS)
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using System;
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using System.Collections.Generic;
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using UnityEngine;
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using Unity.Collections;
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using Unity.Jobs;
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using Unity.Mathematics;
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using Unity.Burst;
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using System.Runtime.CompilerServices;
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using Unity.Collections.LowLevel.Unsafe;
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using System.Threading;
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namespace Obi
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{
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public static class BurstMath
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{
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public const float epsilon = 0.0000001f;
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public const float zero = 0;
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public const float one = 1;
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public static readonly float golden = (math.sqrt(5.0f) + 1) / 2.0f;
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public static unsafe void AddRange<T, U>(this NativeList<T> dst, U[] array) where T : unmanaged where U : unmanaged
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{
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var tsize = sizeof(T);
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var usize = sizeof(U);
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if (tsize == usize)
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{
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int dstIndex = dst.Length;
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dst.ResizeUninitialized(dst.Length + array.Length);
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fixed (U* srcPtr = array)
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{
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var dstPtr = (T*)dst.GetUnsafePtr() + dstIndex;
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UnsafeUtility.MemCpy(dstPtr, srcPtr, usize * array.Length);
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}
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}
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}
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public static unsafe void AddReplicate<T, U>(this NativeList<T> dst, U value, int length) where T : unmanaged where U : unmanaged
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{
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var tsize = sizeof(T);
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var usize = sizeof(U);
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if (tsize == usize)
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{
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int dstIndex = dst.Length;
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dst.ResizeUninitialized(dst.Length + length);
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var dstPtr = (T*)dst.GetUnsafePtr() + dstIndex;
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var srcPtr = UnsafeUtility.AddressOf(ref value);
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UnsafeUtility.MemCpyReplicate(dstPtr, srcPtr, tsize, length);
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}
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}
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public static float AtomicAdd(ref float location, float value)
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{
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float newCurrentValue = location;
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while (true)
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{
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float currentValue = newCurrentValue;
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float newValue = currentValue + value;
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newCurrentValue = Interlocked.CompareExchange(ref location, newValue, currentValue);
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if (newCurrentValue.Equals(currentValue))
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return newValue;
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public unsafe static void AtomicAdd(NativeArray<float4> array, int p, float4 data)
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{
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float4* arr = (float4*)array.GetUnsafePtr();
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AtomicAdd(ref arr[p].x, data.x);
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AtomicAdd(ref arr[p].y, data.y);
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AtomicAdd(ref arr[p].z, data.z);
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AtomicAdd(ref arr[p].w, data.w);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public unsafe static void AtomicAdd(NativeArray<float> array, int p, float data)
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{
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float* arr = (float*)array.GetUnsafePtr();
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AtomicAdd(ref arr[p], data);
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}
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// multiplies a column vector by a row vector.
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3x3 multrnsp(in float4 column, in float4 row)
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{
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return new float3x3(column.xyz * row[0], column.xyz * row[1], column.xyz * row[2]);
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}
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// multiplies a column vector by a row vector.
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4x4 multrnsp4(in float4 column, float4 row)
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{
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row[3] = 0;
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return new float4x4(column * row[0], column * row[1], column * row[2], float4.zero);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 project(this float4 vector, float4 onto)
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{
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float len = math.lengthsq(onto);
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if (len < epsilon)
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return float4.zero;
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return math.dot(onto, vector) * onto / len;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3 project(this float3 vector, float3 onto)
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{
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float len = math.lengthsq(onto);
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if (len < epsilon)
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return float3.zero;
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return math.dot(onto, vector) * onto / len;
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}
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/*[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 GetInvParticleInertiaTensor(float4 principalRadii, float invRotationalMass)
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{
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float4 sqrRadii = principalRadii * principalRadii;
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return new float4(5 * invRotationalMass / math.max(new float3(sqrRadii[1] + sqrRadii[2],
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sqrRadii[0] + sqrRadii[2],
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sqrRadii[0] + sqrRadii[1]), epsilon), 0);
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}*/
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 GetParticleInertiaTensor(float4 principalRadii, float invRotationalMass)
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{
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float4 sqrRadii = principalRadii * principalRadii;
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return 0.2f / (invRotationalMass + epsilon) * new float4(sqrRadii[1] + sqrRadii[2],
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sqrRadii[0] + sqrRadii[2],
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sqrRadii[0] + sqrRadii[1], 0);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4x4 TransformInertiaTensor(float4 tensor, quaternion rotation)
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{
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float4x4 rotMatrix = rotation.toMatrix();
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return math.mul(rotMatrix, math.mul(tensor.asDiagonal(), math.transpose(rotMatrix)));
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float RotationalInvMass(float4x4 inverseInertiaTensor, float4 point, float4 direction)
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{
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float4 cr = math.mul(inverseInertiaTensor, new float4(math.cross(point.xyz, direction.xyz), 0));
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return math.dot(math.cross(cr.xyz, point.xyz), direction.xyz);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 GetParticleVelocityAtPoint(float4 position, float4 prevPosition, float4 point, float dt)
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{
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// no angular velocity, so calculate and return linear velocity only:
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return BurstIntegration.DifferentiateLinear(position, prevPosition, dt);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 GetParticleVelocityAtPoint(float4 position, float4 prevPosition, quaternion orientation, quaternion prevOrientation, float4 point, float dt)
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{
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// calculate both linear and angular velocities:
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float4 linearVelocity = BurstIntegration.DifferentiateLinear(position, prevPosition, dt);
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float4 angularVelocity = BurstIntegration.DifferentiateAngular(orientation, prevOrientation, dt);
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return linearVelocity + new float4(math.cross(angularVelocity.xyz, (point - prevPosition).xyz), 0);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 GetRigidbodyVelocityAtPoint(int rigidbodyIndex,
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float4 point,
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NativeArray<BurstRigidbody> rigidbodies,
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NativeArray<float4> linearDeltas,
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NativeArray<float4> angularDeltas,
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BurstInertialFrame solverToWorld)
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{
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float4 linear = rigidbodies[rigidbodyIndex].velocity + linearDeltas[rigidbodyIndex];
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float4 angular = rigidbodies[rigidbodyIndex].angularVelocity + angularDeltas[rigidbodyIndex];
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float4 r = solverToWorld.frame.TransformPoint(point) - rigidbodies[rigidbodyIndex].com;
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// calculate rigidbody velocity:
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float4 wsRigidbodyVelocity = linear + new float4(math.cross(angular.xyz, r.xyz), 0);
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// calculate solver velocity:
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float4 wsSolverVelocity = solverToWorld.velocity + new float4(math.cross(solverToWorld.angularVelocity.xyz, point.xyz), 0);
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// convert the resulting velocity back to solver space:
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return solverToWorld.frame.InverseTransformVector(wsRigidbodyVelocity - wsSolverVelocity);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 GetRigidbodyVelocityAtPoint(int rigidbodyIndex,
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float4 point,
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NativeArray<BurstRigidbody> rigidbodies,
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BurstInertialFrame solverToWorld)
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{
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float4 linear = rigidbodies[rigidbodyIndex].velocity;
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float4 angular = rigidbodies[rigidbodyIndex].angularVelocity;
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float4 r = solverToWorld.frame.TransformPoint(point) - rigidbodies[rigidbodyIndex].com;
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// calculate rigidbody velocity:
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float4 wsRigidbodyVelocity = linear + new float4(math.cross(angular.xyz, r.xyz), 0);
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// calculate solver velocity:
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float4 wsSolverVelocity = solverToWorld.velocity + new float4(math.cross(solverToWorld.angularVelocity.xyz, point.xyz), 0);
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// Point is assumed to be expressed in solver space. Since rigidbodies are expressed in world space, we need to convert the
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// point to world space, and convert the resulting velocity back to solver space.
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return solverToWorld.frame.InverseTransformVector(wsRigidbodyVelocity - wsSolverVelocity);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void ApplyImpulse(int rigidbodyIndex,
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float4 impulse,
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float4 point,
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NativeArray<BurstRigidbody> rigidbodies,
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NativeArray<float4> linearDeltas,
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NativeArray<float4> angularDeltas,
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BurstAffineTransform solverToWorld)
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{
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float4 impulseWS = solverToWorld.TransformVector(impulse);
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float4 r = solverToWorld.TransformPoint(point) - rigidbodies[rigidbodyIndex].com;
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float4 linearDelta = rigidbodies[rigidbodyIndex].inverseMass * impulseWS;
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float4 angularDelta = math.mul(rigidbodies[rigidbodyIndex].inverseInertiaTensor, new float4(math.cross(r.xyz, impulseWS.xyz), 0));
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AtomicAdd(linearDeltas, rigidbodyIndex, linearDelta);
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AtomicAdd(angularDeltas, rigidbodyIndex, angularDelta);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void ApplyDeltaQuaternion(int rigidbodyIndex,
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quaternion rotation,
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quaternion delta,
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NativeArray<float4> angularDeltas,
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BurstAffineTransform solverToWorld,
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float dt)
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{
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quaternion rotationWS = math.mul(solverToWorld.rotation, rotation);
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quaternion deltaWS = math.mul(solverToWorld.rotation, delta);
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// convert quaternion delta to angular acceleration:
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quaternion newRotation = math.normalize(new quaternion(rotationWS.value + deltaWS.value));
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AtomicAdd(angularDeltas, rigidbodyIndex, BurstIntegration.DifferentiateAngular(newRotation, rotationWS, dt));
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void OneSidedNormal(float4 forward, ref float4 normal)
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{
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float dot = math.dot(normal.xyz, forward.xyz);
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if (dot < 0) normal -= 2 * dot * forward;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float EllipsoidRadius(float4 normSolverDirection, quaternion orientation, float3 radii)
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{
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float3 localDir = math.mul(math.conjugate(orientation), normSolverDirection.xyz);
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float sqrNorm = math.lengthsq(localDir / radii);
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return sqrNorm > epsilon ? math.sqrt(1 / sqrNorm) : radii.x;
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}
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public static quaternion ExtractRotation(float4x4 matrix, quaternion rotation, int iterations)
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{
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return ExtractRotation((float3x3)matrix, rotation, iterations);
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}
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public static quaternion ExtractRotation(float3x3 matrix, quaternion rotation, int iterations)
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{
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float3x3 R;
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for (int i = 0; i < iterations; ++i)
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{
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R = rotation.toMatrix3();
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float3 omega = (math.cross(R.c0, matrix.c0) + math.cross(R.c1, matrix.c1) + math.cross(R.c2, matrix.c2)) /
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(math.abs(math.dot(R.c0, matrix.c0) + math.dot(R.c1, matrix.c1) + math.dot(R.c2, matrix.c2)) + epsilon);
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float w = math.length(omega);
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if (w < epsilon)
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break;
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rotation = math.normalize(math.mul(quaternion.AxisAngle((1.0f / w) * omega, w), rotation));
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}
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return rotation;
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}
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// decomposes a quaternion in swing and twist around a given axis:
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void SwingTwist(quaternion q, float3 twistAxis, out quaternion swing, out quaternion twist)
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{
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float dot = math.dot(q.value.xyz, twistAxis);
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float3 p = twistAxis * dot;
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twist = math.normalizesafe(new quaternion(p[0], p[1], p[2], q.value.w));
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swing = math.mul(q, math.conjugate(twist));
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}
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public static float4x4 toMatrix(this quaternion q)
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{
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float xx = q.value.x * q.value.x;
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float xy = q.value.x * q.value.y;
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float xz = q.value.x * q.value.z;
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float xw = q.value.x * q.value.w;
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float yy = q.value.y * q.value.y;
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float yz = q.value.y * q.value.z;
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float yw = q.value.y * q.value.w;
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float zz = q.value.z * q.value.z;
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float zw = q.value.z * q.value.w;
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return new float4x4(1 - 2 * (yy + zz), 2 * (xy - zw), 2 * (xz + yw), 0,
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2 * (xy + zw), 1 - 2 * (xx + zz), 2 * (yz - xw), 0,
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2 * (xz - yw), 2 * (yz + xw), 1 - 2 * (xx + yy), 0,
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0, 0, 0, 1);
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}
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public static float3x3 toMatrix3(this quaternion q)
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{
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float xx = q.value.x * q.value.x;
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float xy = q.value.x * q.value.y;
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float xz = q.value.x * q.value.z;
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float xw = q.value.x * q.value.w;
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float yy = q.value.y * q.value.y;
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float yz = q.value.y * q.value.z;
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float yw = q.value.y * q.value.w;
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float zz = q.value.z * q.value.z;
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float zw = q.value.z * q.value.w;
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return new float3x3(1 - 2 * (yy + zz), 2 * (xy - zw), 2 * (xz + yw),
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2 * (xy + zw), 1 - 2 * (xx + zz), 2 * (yz - xw),
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2 * (xz - yw), 2 * (yz + xw), 1 - 2 * (xx + yy));
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4x4 asDiagonal(this float4 v)
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{
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return new float4x4(v.x, 0, 0, 0,
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0, v.y, 0, 0,
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0, 0, v.z, 0,
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0, 0, 0, v.w);
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}
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/**
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* Modulo operator that also follows intuition for negative arguments. That is , -1 mod 3 = 2, not -1.
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*/
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float3 nfmod(float3 a, float3 b)
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{
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return a - b * math.floor(a / b);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float4 diagonal(this float4x4 value)
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{
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return new float4(value.c0[0], value.c1[1], value.c2[2], value.c3[3]);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static float frobeniusNorm(this float4x4 m)
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{
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return math.sqrt(math.lengthsq(m.c0) + math.lengthsq(m.c1) + math.lengthsq(m.c2) + math.lengthsq(m.c3));
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}
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public static void EigenSolve(float3x3 D, out float3 S, out float3x3 V)
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{
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// D is symmetric
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// S is a vector whose elements are eigenvalues
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// V is a matrix whose columns are eigenvectors
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S = EigenValues(D);
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float3 V0, V1, V2;
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if (S[0] - S[1] > S[1] - S[2])
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{
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V0 = EigenVector(D, S[0]);
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if (S[1] - S[2] < math.FLT_MIN_NORMAL)
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{
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V2 = V0.unitOrthogonal();
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}
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else
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{
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V2 = EigenVector(D, S[2]); V2 -= V0 * math.dot(V0, V2); V2 = math.normalize(V2);
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}
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V1 = math.cross(V2, V0);
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}
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else
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{
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V2 = EigenVector(D, S[2]);
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if (S[0] - S[1] < math.FLT_MIN_NORMAL)
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{
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V1 = V2.unitOrthogonal();
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}
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else
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{
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V1 = EigenVector(D, S[1]); V1 -= V2 * math.dot(V2, V1); V1 = math.normalize(V1);
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}
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V0 = math.cross(V1, V2);
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}
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V.c0 = V0;
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V.c1 = V1;
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V.c2 = V2;
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}
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static float3 unitOrthogonal(this float3 input)
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{
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// Find a vector to cross() the input with.
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if (!(input.x < input.z * epsilon)
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|| !(input.y < input.z * epsilon))
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{
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float invnm = 1 / math.length(input.xy);
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return new float3(-input.y * invnm, input.x * invnm, 0);
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}
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else
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{
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float invnm = 1 / math.length(input.yz);
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return new float3(0, -input.z * invnm, input.y * invnm);
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}
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}
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// D is symmetric, S is an eigen value
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static float3 EigenVector(float3x3 D, float S)
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{
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// Compute a cofactor matrix of D - sI.
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float3 c0 = D.c0; c0[0] -= S;
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float3 c1 = D.c1; c1[1] -= S;
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float3 c2 = D.c2; c2[2] -= S;
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// Upper triangular matrix
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float3 c0p = new float3(c1[1] * c2[2] - c2[1] * c2[1], 0, 0);
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float3 c1p = new float3(c2[1] * c2[0] - c1[0] * c2[2], c0[0] * c2[2] - c2[0] * c2[0], 0);
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float3 c2p = new float3(c1[0] * c2[1] - c1[1] * c2[0], c1[0] * c2[0] - c0[0] * c2[1], c0[0] * c1[1] - c1[0] * c1[0]);
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// Get a column vector with a largest norm (non-zero).
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float C01s = c1p[0] * c1p[0];
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float C02s = c2p[0] * c2p[0];
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float C12s = c2p[1] * c2p[1];
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float3 norm = new float3(c0p[0] * c0p[0] + C01s + C02s,
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C01s + c1p[1] * c1p[1] + C12s,
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C02s + C12s + c2p[2] * c2p[2]);
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// index of largest:
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int index = 0;
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if (norm[0] > norm[1] && norm[0] > norm[2])
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index = 0;
|
|
else if (norm[1] > norm[0] && norm[1] > norm[2])
|
|
index = 1;
|
|
else
|
|
index = 2;
|
|
|
|
float3 V = float3.zero;
|
|
|
|
// special case
|
|
if (norm[index] < math.FLT_MIN_NORMAL)
|
|
{
|
|
V[0] = 1; return V;
|
|
}
|
|
|
|
if (index == 0)
|
|
{
|
|
V[0] = c0p[0]; V[1] = c1p[0]; V[2] = c2p[0];
|
|
}
|
|
else if (index == 1)
|
|
{
|
|
V[0] = c1p[0]; V[1] = c1p[1]; V[2] = c2p[1];
|
|
}
|
|
else
|
|
{
|
|
V = c2p;
|
|
}
|
|
return math.normalize(V);
|
|
}
|
|
|
|
static float3 EigenValues(float3x3 D)
|
|
{
|
|
float one_third = 1 / 3.0f;
|
|
float one_sixth = 1 / 6.0f;
|
|
float three_sqrt = math.sqrt(3.0f);
|
|
|
|
float3 c0 = D.c0;
|
|
float3 c1 = D.c1;
|
|
float3 c2 = D.c2;
|
|
|
|
float m = one_third * (c0[0] + c1[1] + c2[2]);
|
|
|
|
// K is D - I*diag(S)
|
|
float K00 = c0[0] - m;
|
|
float K11 = c1[1] - m;
|
|
float K22 = c2[2] - m;
|
|
|
|
float K01s = c1[0] * c1[0];
|
|
float K02s = c2[0] * c2[0];
|
|
float K12s = c2[1] * c2[1];
|
|
|
|
float q = 0.5f * (K00 * (K11 * K22 - K12s) - K22 * K01s - K11 * K02s) + c1[0] * c2[1] * c0[2];
|
|
float p = one_sixth * (K00 * K00 + K11 * K11 + K22 * K22 + 2 * (K01s + K02s + K12s));
|
|
|
|
float p_sqrt = math.sqrt(p);
|
|
|
|
float tmp = p * p * p - q * q;
|
|
float phi = one_third * math.atan2(math.sqrt(math.max(0, tmp)), q);
|
|
float phi_c = math.cos(phi);
|
|
float phi_s = math.sin(phi);
|
|
float sqrt_p_c_phi = p_sqrt * phi_c;
|
|
float sqrt_p_3_s_phi = p_sqrt * three_sqrt * phi_s;
|
|
|
|
float e0 = m + 2 * sqrt_p_c_phi;
|
|
float e1 = m - sqrt_p_c_phi - sqrt_p_3_s_phi;
|
|
float e2 = m - sqrt_p_c_phi + sqrt_p_3_s_phi;
|
|
|
|
float aux;
|
|
if (e0 > e1)
|
|
{
|
|
aux = e0;
|
|
e0 = e1;
|
|
e1 = aux;
|
|
}
|
|
if (e0 > e2)
|
|
{
|
|
aux = e0;
|
|
e0 = e2;
|
|
e2 = aux;
|
|
}
|
|
if (e1 > e2)
|
|
{
|
|
aux = e1;
|
|
e1 = e2;
|
|
e2 = aux;
|
|
}
|
|
|
|
return new float3(e2, e1, e0);
|
|
}
|
|
|
|
public struct CachedTri
|
|
{
|
|
public float4 vertex;
|
|
public float4 edge0;
|
|
public float4 edge1;
|
|
public float4 data;
|
|
|
|
public void Cache(float4 v1,
|
|
float4 v2,
|
|
float4 v3)
|
|
{
|
|
vertex = v1;
|
|
edge0 = v2 - v1;
|
|
edge1 = v3 - v1;
|
|
data = float4.zero;
|
|
data[0] = math.dot(edge0, edge0);
|
|
data[1] = math.dot(edge0, edge1);
|
|
data[2] = math.dot(edge1, edge1);
|
|
data[3] = data[0] * data[2] - data[1] * data[1];
|
|
}
|
|
}
|
|
|
|
public static float4 NearestPointOnTri(in CachedTri tri,
|
|
float4 p,
|
|
out float4 bary)
|
|
{
|
|
float4 v0 = tri.vertex - p;
|
|
float b0 = math.dot(tri.edge0, v0);
|
|
float b1 = math.dot(tri.edge1, v0);
|
|
float t0 = tri.data[1] * b1 - tri.data[2] * b0;
|
|
float t1 = tri.data[1] * b0 - tri.data[0] * b1;
|
|
|
|
if (t0 + t1 <= tri.data[3])
|
|
{
|
|
if (t0 < zero)
|
|
{
|
|
if (t1 < zero) // region 4
|
|
{
|
|
if (b0 < zero)
|
|
{
|
|
t1 = zero;
|
|
if (-b0 >= tri.data[0]) // V0
|
|
t0 = one;
|
|
else // E01
|
|
t0 = -b0 / tri.data[0];
|
|
}
|
|
else
|
|
{
|
|
t0 = zero;
|
|
if (b1 >= zero) // V0
|
|
t1 = zero;
|
|
else if (-b1 >= tri.data[2]) // V2
|
|
t1 = one;
|
|
else // E20
|
|
t1 = -b1 / tri.data[2];
|
|
}
|
|
}
|
|
else // region 3
|
|
{
|
|
t0 = zero;
|
|
if (b1 >= zero) // V0
|
|
t1 = zero;
|
|
else if (-b1 >= tri.data[2]) // V2
|
|
t1 = one;
|
|
else // E20
|
|
t1 = -b1 / tri.data[2];
|
|
}
|
|
}
|
|
else if (t1 < zero) // region 5
|
|
{
|
|
t1 = zero;
|
|
if (b0 >= zero) // V0
|
|
t0 = zero;
|
|
else if (-b0 >= tri.data[0]) // V1
|
|
t0 = one;
|
|
else // E01
|
|
t0 = -b0 / tri.data[0];
|
|
}
|
|
else // region 0, interior
|
|
{
|
|
float invDet = one / tri.data[3];
|
|
t0 *= invDet;
|
|
t1 *= invDet;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
float tmp0, tmp1, numer, denom;
|
|
|
|
if (t0 < zero) // region 2
|
|
{
|
|
tmp0 = tri.data[1] + b0;
|
|
tmp1 = tri.data[2] + b1;
|
|
if (tmp1 > tmp0)
|
|
{
|
|
numer = tmp1 - tmp0;
|
|
denom = tri.data[0] - 2 * tri.data[1] + tri.data[2];
|
|
if (numer >= denom) // V1
|
|
{
|
|
t0 = one;
|
|
t1 = zero;
|
|
}
|
|
else // E12
|
|
{
|
|
t0 = numer / denom;
|
|
t1 = one - t0;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
t0 = zero;
|
|
if (tmp1 <= zero) // V2
|
|
t1 = one;
|
|
else if (b1 >= zero) // V0
|
|
t1 = zero;
|
|
else // E20
|
|
t1 = -b1 / tri.data[2];
|
|
}
|
|
}
|
|
else if (t1 < zero) // region 6
|
|
{
|
|
tmp0 = tri.data[1] + b1;
|
|
tmp1 = tri.data[0] + b0;
|
|
if (tmp1 > tmp0)
|
|
{
|
|
numer = tmp1 - tmp0;
|
|
denom = tri.data[0] - 2 * tri.data[1] + tri.data[2];
|
|
if (numer >= denom) // V2
|
|
{
|
|
t1 = one;
|
|
t0 = zero;
|
|
}
|
|
else // E12
|
|
{
|
|
t1 = numer / denom;
|
|
t0 = one - t1;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
t1 = zero;
|
|
if (tmp1 <= zero) // V1
|
|
t0 = one;
|
|
else if (b0 >= zero) // V0
|
|
t0 = zero;
|
|
else // E01
|
|
t0 = -b0 / tri.data[0];
|
|
}
|
|
}
|
|
else // region 1
|
|
{
|
|
numer = tri.data[2] + b1 - tri.data[1] - b0;
|
|
if (numer <= zero) // V2
|
|
{
|
|
t0 = zero;
|
|
t1 = one;
|
|
}
|
|
else
|
|
{
|
|
denom = tri.data[0] - 2 * tri.data[1] + tri.data[2];
|
|
if (numer >= denom) // V1
|
|
{
|
|
t0 = one;
|
|
t1 = zero;
|
|
}
|
|
else // 12
|
|
{
|
|
t0 = numer / denom;
|
|
t1 = one - t0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
bary = new float4(1 - (t0 + t1), t0, t1,0);
|
|
return tri.vertex + t0 * tri.edge0 + t1 * tri.edge1;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4 NearestPointOnEdge(float4 a, float4 b, float4 p, out float mu, bool clampToSegment = true)
|
|
{
|
|
float4 ap = p - a;
|
|
float4 ab = b - a;
|
|
|
|
mu = math.dot(ap, ab) / math.dot(ab, ab);
|
|
|
|
if (clampToSegment)
|
|
mu = math.saturate(mu);
|
|
|
|
return a + ab * mu;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float3 NearestPointOnEdge(float3 a, float3 b, float3 p, out float mu, bool clampToSegment = true)
|
|
{
|
|
float3 ap = p - a;
|
|
float3 ab = b - a;
|
|
|
|
mu = math.dot(ap, ab) / math.dot(ab, ab);
|
|
|
|
if (clampToSegment)
|
|
mu = math.saturate(mu);
|
|
|
|
return a + ab * mu;
|
|
}
|
|
|
|
public static float4 NearestPointsTwoEdges(float4 a, float4 b, float4 c, float4 d, out float mu1, out float mu2)
|
|
{
|
|
float4 dc = d - c;
|
|
float lineDirSqrMag = math.dot(dc, dc);
|
|
float4 inPlaneA = a - (math.dot(a - c, dc) / lineDirSqrMag * dc);
|
|
float4 inPlaneB = b - (math.dot(b - c, dc) / lineDirSqrMag * dc);
|
|
|
|
float4 inPlaneBA = inPlaneB - inPlaneA;
|
|
float t = math.dot(c - inPlaneA, inPlaneBA) / math.dot(inPlaneBA, inPlaneBA);
|
|
|
|
//t = (inPlaneA != inPlaneB) ? t : 0f; // Zero's t if parallel
|
|
float4 segABtoLineCD = math.lerp(a, b, math.saturate(t));
|
|
|
|
float4 segCDtoSegAB = NearestPointOnEdge(c, d, segABtoLineCD, out mu1);
|
|
float4 segABtoSegCD = NearestPointOnEdge(a, b, segCDtoSegAB, out mu2);
|
|
|
|
return segCDtoSegAB;
|
|
}
|
|
|
|
public static float4 BaryCoords(in float4 A,
|
|
in float4 B,
|
|
in float4 C,
|
|
in float4 P)
|
|
{
|
|
|
|
// Compute vectors
|
|
float4 v0 = C - A;
|
|
float4 v1 = B - A;
|
|
float4 v2 = P - A;
|
|
|
|
// Compute dot products
|
|
float dot00 = math.dot(v0, v0);
|
|
float dot01 = math.dot(v0, v1);
|
|
float dot02 = math.dot(v0, v2);
|
|
float dot11 = math.dot(v1, v1);
|
|
float dot12 = math.dot(v1, v2);
|
|
|
|
// Compute barycentric coordinates
|
|
float det = dot00 * dot11 - dot01 * dot01;
|
|
if (math.abs(det) > epsilon)
|
|
{
|
|
float u = (dot11 * dot02 - dot01 * dot12) / det;
|
|
float v = (dot00 * dot12 - dot01 * dot02) / det;
|
|
return new float4(1 - u - v, v, u, 0);
|
|
}
|
|
return float4.zero;
|
|
|
|
}
|
|
|
|
public static float4 BaryCoords2(in float4 A,
|
|
in float4 B,
|
|
in float4 P)
|
|
{
|
|
float4 v0 = P - A;
|
|
float4 v1 = B - A;
|
|
float y = math.sqrt(math.dot(v0, v0) / (math.dot(v1, v1) + epsilon));
|
|
return new float4(1 - y, y, 0, 0);
|
|
}
|
|
|
|
public static float4 BaryIntrpl(in float4 p1, in float4 p2, in float4 p3, in float4 coords)
|
|
{
|
|
return coords[0] * p1 + coords[1] * p2 + coords[2] * p3;
|
|
}
|
|
|
|
public static float4 BaryIntrpl(in float4 p1, in float4 p2, in float4 coords)
|
|
{
|
|
return coords[0] * p1 + coords[1] * p2;
|
|
}
|
|
|
|
public static float BaryIntrpl(float p1, float p2, float p3, float4 coords)
|
|
{
|
|
return coords[0] * p1 + coords[1] * p2 + coords[2] * p3;
|
|
}
|
|
|
|
public static float BaryIntrpl(float p1, float p2, float4 coords)
|
|
{
|
|
return coords[0] * p1 + coords[1] * p2;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float BaryScale(float4 coords)
|
|
{
|
|
return 1.0f / math.dot(coords, coords);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4 BarycenterForSimplexOfSize(int simplexSize)
|
|
{
|
|
float value = 1f / simplexSize;
|
|
float4 center = float4.zero;
|
|
for (int i = 0; i < simplexSize; ++i)
|
|
center[i] = value;
|
|
return center;
|
|
}
|
|
|
|
// https://fgiesen.wordpress.com/2009/12/13/decoding-morton-codes/
|
|
|
|
// "Insert" a 0 bit after each of the 16 low bits of x
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint Part1By1(uint x)
|
|
{
|
|
x &= 0x0000ffff; // x = ---- ---- ---- ---- fedc ba98 7654 3210
|
|
x = (x ^ (x << 8)) & 0x00ff00ff; // x = ---- ---- fedc ba98 ---- ---- 7654 3210
|
|
x = (x ^ (x << 4)) & 0x0f0f0f0f; // x = ---- fedc ---- ba98 ---- 7654 ---- 3210
|
|
x = (x ^ (x << 2)) & 0x33333333; // x = --fe --dc --ba --98 --76 --54 --32 --10
|
|
x = (x ^ (x << 1)) & 0x55555555; // x = -f-e -d-c -b-a -9-8 -7-6 -5-4 -3-2 -1-0
|
|
return x;
|
|
}
|
|
|
|
|
|
// "Insert" two 0 bits after each of the 10 low bits of x
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint Part1By2(uint x)
|
|
{
|
|
x &= 0x000003ff; // x = ---- ---- ---- ---- ---- --98 7654 3210
|
|
x = (x ^ (x << 16)) & 0xff0000ff; // x = ---- --98 ---- ---- ---- ---- 7654 3210
|
|
x = (x ^ (x << 8)) & 0x0300f00f; // x = ---- --98 ---- ---- 7654 ---- ---- 3210
|
|
x = (x ^ (x << 4)) & 0x030c30c3; // x = ---- --98 ---- 76-- --54 ---- 32-- --10
|
|
x = (x ^ (x << 2)) & 0x09249249; // x = ---- 9--8 --7- -6-- 5--4 --3- -2-- 1--0
|
|
return x;
|
|
}
|
|
|
|
// Inverse of Part1By1 - "delete" all odd-indexed bits
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint Compact1By1(uint x)
|
|
{
|
|
x &= 0x55555555; // x = -f-e -d-c -b-a -9-8 -7-6 -5-4 -3-2 -1-0
|
|
x = (x ^ (x >> 1)) & 0x33333333; // x = --fe --dc --ba --98 --76 --54 --32 --10
|
|
x = (x ^ (x >> 2)) & 0x0f0f0f0f; // x = ---- fedc ---- ba98 ---- 7654 ---- 3210
|
|
x = (x ^ (x >> 4)) & 0x00ff00ff; // x = ---- ---- fedc ba98 ---- ---- 7654 3210
|
|
x = (x ^ (x >> 8)) & 0x0000ffff; // x = ---- ---- ---- ---- fedc ba98 7654 3210
|
|
return x;
|
|
}
|
|
|
|
// Inverse of Part1By2 - "delete" all bits not at positions divisible by 3
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint Compact1By2(uint x)
|
|
{
|
|
x &= 0x09249249; // x = ---- 9--8 --7- -6-- 5--4 --3- -2-- 1--0
|
|
x = (x ^ (x >> 2)) & 0x030c30c3; // x = ---- --98 ---- 76-- --54 ---- 32-- --10
|
|
x = (x ^ (x >> 4)) & 0x0300f00f; // x = ---- --98 ---- ---- 7654 ---- ---- 3210
|
|
x = (x ^ (x >> 8)) & 0xff0000ff; // x = ---- --98 ---- ---- ---- ---- 7654 3210
|
|
x = (x ^ (x >> 16)) & 0x000003ff; // x = ---- ---- ---- ---- ---- --98 7654 3210
|
|
return x;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint EncodeMorton2(uint2 coords)
|
|
{
|
|
return (Part1By1(coords.y) << 1) + Part1By1(coords.x);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint EncodeMorton3(uint3 coords)
|
|
{
|
|
return (Part1By2(coords.z) << 2) + (Part1By2(coords.y) << 1) + Part1By2(coords.x);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint3 DecodeMorton2(uint code)
|
|
{
|
|
return new uint3(Compact1By1(code >> 0), Compact1By1(code >> 1), 0);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static uint3 DecodeMorton3(uint code)
|
|
{
|
|
return new uint3(Compact1By2(code >> 0), Compact1By2(code >> 1), Compact1By2(code >> 2));
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float4 UnpackFloatRGBA(float v)
|
|
{
|
|
uint rgba = math.asuint(v);
|
|
float r = ((rgba & 0xff000000) >> 24) / 255f;
|
|
float g = ((rgba & 0x00ff0000) >> 16) / 255f;
|
|
float b = ((rgba & 0x0000ff00) >> 8) / 255f;
|
|
float a = (rgba & 0x000000ff) / 255f;
|
|
return new float4(r, g, b, a);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float PackFloatRGBA(float4 enc)
|
|
{
|
|
uint rgba = ((uint)(enc.x * 255f) << 24) +
|
|
((uint)(enc.y * 255f) << 16) +
|
|
((uint)(enc.z * 255f) << 8) +
|
|
(uint)(enc.w * 255f);
|
|
return math.asfloat(rgba);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float2 UnpackFloatRG(float v)
|
|
{
|
|
uint rgba = math.asuint(v);
|
|
float r = ((rgba & 0xffff0000) >> 16) / 65535f;
|
|
float g = (rgba & 0x0000ffff) / 65535f;
|
|
return new float2(r, g);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static float PackFloatRG(float2 enc)
|
|
{
|
|
uint rgba = ((uint)(enc.x * 65535f) << 16) +
|
|
(uint)(enc.y * 65535f);
|
|
return math.asfloat(rgba);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
static float2 OctWrap(float2 v)
|
|
{
|
|
return (1.0f - math.abs(v.yx)) * new float2(v.x >= 0.0f ? 1.0f : -1.0f, v.y >= 0.0f ? 1.0f : -1.0f);
|
|
}
|
|
|
|
// use octahedral encoding to reduce to 2 coords, then pack them as two 16 bit values in a 32 bit float.
|
|
public static float OctEncode(float3 n)
|
|
{
|
|
n /= math.abs(n.x) + math.abs(n.y) + math.abs(n.z);
|
|
n.xy = n.z >= 0.0 ? n.xy : OctWrap(n.xy);
|
|
n.xy = n.xy * 0.5f + 0.5f;
|
|
|
|
uint nx = (uint)(n.x * 0xffff);
|
|
uint ny = (uint)(n.y * 0xffff);
|
|
return math.asfloat((nx << 16) | (ny & 0xffff));
|
|
}
|
|
|
|
public static float3 OctDecode(float k)
|
|
{
|
|
uint d = math.asuint(k);
|
|
float2 f = new float2((d >> 16) / 65535f, (d & 0xffff) / 65535f) * 2f - 1f;
|
|
|
|
float3 n = new float3(f.x, f.y, 1.0f - math.abs(f.x) - math.abs(f.y));
|
|
float t = math.saturate(-n.z);
|
|
n.x += n.x >= 0.0f ? -t : t;
|
|
n.y += n.y >= 0.0f ? -t : t;
|
|
return math.normalize(n);
|
|
}
|
|
|
|
public static float Remap01(float value, float min_, float max_)
|
|
{
|
|
return (math.min(value, max_) - math.min(value, min_)) / (max_ - min_);
|
|
}
|
|
|
|
public static float3 Sort(this float3 f)
|
|
{
|
|
float aux;
|
|
if (f.x > f.y)
|
|
{
|
|
aux = f.x;
|
|
f.x = f.y;
|
|
f.y = aux;
|
|
}
|
|
if (f.x > f.z)
|
|
{
|
|
aux = f.x;
|
|
f.x = f.z;
|
|
f.z = aux;
|
|
}
|
|
if (f.y > f.z)
|
|
{
|
|
aux = f.y;
|
|
f.y = f.z;
|
|
f.z = aux;
|
|
}
|
|
return new float3(f.z,f.y,f.x);
|
|
}
|
|
|
|
public static unsafe void RemoveRangeBurst<T>(this NativeList<T> list, int index, int count)
|
|
where T : unmanaged
|
|
{
|
|
#if ENABLE_UNITY_COLLECTIONS_CHECKS
|
|
if ((uint)index >= (uint)list.Length)
|
|
{
|
|
throw new IndexOutOfRangeException(
|
|
$"Index {index} is out of range in NativeList of '{list.Length}' Length.");
|
|
}
|
|
#endif
|
|
|
|
int elemSize = UnsafeUtility.SizeOf<T>();
|
|
byte* basePtr = (byte*)list.GetUnsafePtr();
|
|
|
|
UnsafeUtility.MemMove(basePtr + (index * elemSize), basePtr + ((index + count) * elemSize), elemSize * (list.Length - count - index));
|
|
|
|
// No easy way to change length so we just loop this unfortunately.
|
|
for (var i = 0; i < count; i++)
|
|
{
|
|
list.RemoveAtSwapBack(list.Length - 1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
#endif |