UnrealEngineUWP/Engine/Shaders/Private/IntersectionUtils.ush

// Copyright Epic Games, Inc. All Rights Reserved.

#pragma once

bool SphereIntersectCone(float4 SphereCenterAndRadius, float3 ConeVertex, float3 ConeAxis, float ConeAngleCos, float ConeAngleSin)
{
	float3 U = ConeVertex - (SphereCenterAndRadius.w / ConeAngleSin) * ConeAxis;
	float3 D = SphereCenterAndRadius.xyz - U;
	float DSizeSq = dot(D, D);
	float E = dot(ConeAxis, D);

	if (E > 0 && E * E >= DSizeSq * ConeAngleCos * ConeAngleCos)
	{
		D = SphereCenterAndRadius.xyz - ConeVertex;
		DSizeSq = dot(D, D);
		E = -dot(ConeAxis, D);

		if (E > 0 && E * E >= DSizeSq * ConeAngleSin * ConeAngleSin)
		{
			return DSizeSq <= SphereCenterAndRadius.w * SphereCenterAndRadius.w;
		}
		else
		{
			return true;
		}
	}

	return false;
}

bool SphereIntersectConeWithMaxDistance(float4 SphereCenterAndRadius, float3 ConeVertex, float3 ConeAxis, float ConeAngleCos, float ConeAngleSin, float MaxDistanceAlongAxis)
{
	if (SphereIntersectCone(SphereCenterAndRadius, ConeVertex, ConeAxis, ConeAngleCos, ConeAngleSin))
	{
		float ConeAxisDistance = dot(SphereCenterAndRadius.xyz - ConeVertex, ConeAxis);
		float ConeAxisDistanceMax = ConeAxisDistance - SphereCenterAndRadius.w;

		return ConeAxisDistanceMax < MaxDistanceAlongAxis;
	}

	return false;
}

bool SphereIntersectConeWithDepthRanges(float4 SphereCenterAndRadius, float3 ConeVertex, float3 ConeAxis, float ConeAngleCos, float ConeAngleSin, float4 ConeAxisDepthRanges)
{
	if (SphereIntersectCone(SphereCenterAndRadius, ConeVertex, ConeAxis, ConeAngleCos, ConeAngleSin))
	{
		float ConeAxisDistance = dot(SphereCenterAndRadius.xyz - ConeVertex, ConeAxis);
		float2 ConeAxisDistanceMinMax = float2(ConeAxisDistance + SphereCenterAndRadius.w, ConeAxisDistance - SphereCenterAndRadius.w);

		if ((ConeAxisDistanceMinMax.x > ConeAxisDepthRanges.x && ConeAxisDistanceMinMax.y < ConeAxisDepthRanges.y)
			|| (ConeAxisDistanceMinMax.x > ConeAxisDepthRanges.z && ConeAxisDistanceMinMax.y < ConeAxisDepthRanges.w))
		{
			return true;
		}
	}

	return false;
}

bool SphereIntersectSphere(float4 SphereCenterAndRadius, float4 OtherSphereCenterAndRadius)
{
	float CombinedRadii = SphereCenterAndRadius.w + OtherSphereCenterAndRadius.w;
	float3 VectorBetweenCenters = SphereCenterAndRadius.xyz - OtherSphereCenterAndRadius.xyz;
	return dot(VectorBetweenCenters, VectorBetweenCenters) < CombinedRadii * CombinedRadii;
}