public static (Matrix4x4 view, Matrix4x4 projection, bool inverseZ) PSMProjection(int lightIndex,
MyRenderingData renderingData, ShadowSettings settings)
{
var camera = GameObject.Find("Main Camera").GetComponent <Camera>();
var cameraView = camera.worldToCameraMatrix;
var cameraProjection = GL.GetGPUProjectionMatrix(camera.projectionMatrix, false);
var light = renderingData.cullResults.visibleLights[lightIndex].light;
var p = light.transform.forward.ToVector4(1);
var l = light.transform.forward.ToVector4(0);
var pView = cameraView * p;
var lView = cameraView * l;
var lClip = cameraProjection * lView.ToVector3().normalized.ToVector4(0);
var pClip = cameraProjection * lView.ToVector3().normalized.ToVector4(1);
var lightNDC = lClip / pClip.w;
var lightView = Matrix4x4.LookAt(lightNDC.ToVector3(), Vector3.forward * .5f, Vector3.up).inverse;
var ndcBounds = new Bounds(Vector3.forward * 0.5f, new Vector3(2, 2, 1));
var ndcBoundVerts = new Vector3[8];
for (int x = -1, i = 0; x <= 1; x += 2)
{
for (int y = -1; y <= 1; y += 2)
{
for (int z = -1; z <= 1; z += 2)
{
ndcBoundVerts[i++] = ndcBounds.center + Vector3.Scale(ndcBounds.extents, new Vector3(x, y, z));
}
}
}
var frustum = BestfitFrustum(false, lightView, ndcBoundVerts);
var inverseZ = Vector3.Dot(lView, -lightNDC.ToVector3()) < 0;
if (settings.debug)
{
ShadowUtils.DrawFrustum(frustum, false, lightView.inverse);
ShadowUtils.DrawBound(ndcBounds, Color.magenta);
Debug.DrawLine(Vector3.forward * 0.5f, lightNDC.ToVector3());
}
return(lightView, Matrix4x4.Frustum(frustum), inverseZ);
}
public static Matrix4x4 TSMTransform(Camera camera, Matrix4x4 lightViewProjection,
ShadowSettings shadowSettings)
{
var frustumVerts = ShadowUtils
.GetCameraFrustumVerticies(camera, camera.nearClipPlane, shadowSettings.maxShadowDistance)
.Select(p => ToPostPerspective(p, lightViewProjection));
var convex = GetConvexHull(frustumVerts.Select(p => p.ToVector2()).ToArray());
var nearCenter =
ToPostPerspective(camera.transform.position + camera.transform.forward * camera.nearClipPlane,
lightViewProjection).ToVector2();
var farCenter =
ToPostPerspective(
camera.transform.position + camera.transform.forward * shadowSettings.maxShadowDistance,
lightViewProjection).ToVector2();
var focusPoint =
ToPostPerspective(camera.transform.position + camera.transform.forward * shadowSettings.focusDistance,
lightViewProjection).ToVector2();
var centralLine = farCenter - nearCenter;
var centralLineVector = centralLine.normalized;
var topPoint = nearCenter +
centralLineVector * convex.Min(p => Vector2.Dot(p - nearCenter, centralLineVector));
var bottomVert = convex.MaxOf(p => Vector2.Dot(p - nearCenter, centralLineVector), p => p);
var bottomPoint = topPoint + centralLineVector * Vector2.Dot(bottomVert - topPoint, centralLineVector);
var tangent = (bottomVert - bottomPoint).normalized *
Mathf.Sign(MathUtility.Cross2(bottomVert - topPoint, centralLineVector));
var height = (bottomPoint - topPoint).magnitude;
var focusLen = Vector2.Dot(focusPoint - topPoint, centralLineVector);
var λ = height;
var ξ = -0.6f;
var δ = focusLen;
var η = (λ * δ + λ * δ * ξ) / (λ - 2 * δ - λ * ξ);
var origin = -η * centralLineVector + topPoint;
var cosMaxHalfAngle = convex.Min(p => Vector2.Dot((p - origin).normalized, centralLineVector));
var tan = Mathf.Sqrt(1 - cosMaxHalfAngle * cosMaxHalfAngle) / cosMaxHalfAngle;
var minSinHalfAngle = convex.Min(p => MathUtility.Cross2((p - origin).normalized, centralLineVector));
var maxSinHalfAngle = convex.Max(p => MathUtility.Cross2((p - origin).normalized, centralLineVector));
var minTan = minSinHalfAngle / Mathf.Sqrt(1 - minSinHalfAngle * minSinHalfAngle);
var maxTan = maxSinHalfAngle / Mathf.Sqrt(1 - maxSinHalfAngle * maxSinHalfAngle);
var t0 = bottomPoint + (bottomPoint - origin).magnitude * minTan * tangent;
var t1 = bottomPoint + (bottomPoint - origin).magnitude * maxTan * tangent;
var t2 = topPoint + (topPoint - origin).magnitude * minTan * tangent;
var t3 = topPoint + (topPoint - origin).magnitude * maxTan * tangent;
// Transform trapezoid into unit cube
// Following https://www.comp.nus.edu.sg/~tants/tsm/TSM_recipe.html
var transform = Matrix4x4.identity;
// #1
Vector4 u = (t2 + t3) / 2;
transform = Matrix4x4.Translate(-u) * transform;
// #2
u = (t2 - t3) / (t2 - t3).magnitude;
transform = new Matrix4x4(
new Vector4(u.x, u.y, 0, 0),
new Vector4(u.y, -u.x, 0, 0),
new Vector4(0, 0, 1, 0),
new Vector4(0, 0, 0, 1)
) * transform;
// #3
u = transform * origin.ToVector4(0, 1);
transform = Matrix4x4.Translate(-u) * transform;
// #4
u = (transform.MultiplyPoint((t2 + t3) / 2));
transform = new Matrix4x4(
new Vector4(1, -u.x / u.y, 0, 0),
new Vector4(0, 1, 0, 0),
new Vector4(0, 0, 1, 0),
new Vector4(0, 0, 0, 1)
).transpose *transform;
// #5
u = transform.MultiplyPoint(t2);
transform = Matrix4x4.Scale(new Vector3(1 / u.x, 1 / u.y, 1)) * transform;
// #6
transform = new Matrix4x4(
new Vector4(1, 0, 0, 0),
new Vector4(0, 1, 0, 1),
new Vector4(0, 0, 1, 0),
new Vector4(0, 1, 0, 0)
) * transform;
// #7
u = transform * t0.ToVector4(0, 1);
var v = transform * t2.ToVector4(0, 1);
transform = Matrix4x4.Translate(new Vector3(0, -(u.y / u.w + v.y / v.w) / 2, 0)) * transform;
// #8
u = transform * t0.ToVector4(0, 1);
transform = Matrix4x4.Scale(new Vector3(1, -u.w / u.y, 1)) * transform;
var trapezoidal = new Vector2[] { t0, t1, t3, t2 };
var t = trapezoidal.Select(p => transform.MultiplyPoint(p).ToVector2()).ToArray();
//DrawPolygonOnLightPlane(t, lightViewProjection, Color.blue);
if (shadowSettings.debug)
{
ShadowUtils.DrawPolygonOnLightPlane(trapezoidal, lightViewProjection, Color.blue);
ShadowUtils.DrawPolygonOnLightPlane(new Vector2[] { nearCenter, farCenter }, lightViewProjection, Color.red);
ShadowUtils.DrawPolygonOnLightPlane(convex, lightViewProjection, Color.red);
}
return(transform);
}
public static (Matrix4x4 view, Matrix4x4 projection) GetShadowViewProjection(ShadowSettings settings,
MyRenderingData renderingData, int lightIndex)
{
var camera = renderingData.camera;
if (settings.debug)
{
camera = GameObject.Find("Main Camera").GetComponent <Camera>();
}
var cameraToWorld = camera.transform.localToWorldMatrix;
var p0 = cameraToWorld.MultiplyPoint(new Vector3(0, 0, 0));
var h = Mathf.Tan(camera.fieldOfView * Mathf.Deg2Rad / 2);
var w = h * camera.aspect;
var p1 = cameraToWorld.MultiplyPoint(new Vector3(-w, -h, 1) * settings.maxShadowDistance);
var p2 = cameraToWorld.MultiplyPoint(new Vector3(w, -h, 1) * settings.maxShadowDistance);
var p3 = cameraToWorld.MultiplyPoint(new Vector3(w, h, 1) * settings.maxShadowDistance);
var p4 = cameraToWorld.MultiplyPoint(new Vector3(-w, h, 1) * settings.maxShadowDistance);
//左右手坐标转换
var view = Matrix4x4.Scale(new Vector3(1, 1, -1)) * settings.transform.worldToLocalMatrix;
renderingData.cullResults.GetShadowCasterBounds(lightIndex, out var bounds);
//阴影包围盒
var casterBoundVerts = new Vector3[8];
for (int x = -1, i = 0; x <= 1; x += 2)
{
for (int y = -1; y <= 1; y += 2)
{
for (int z = -1; z <= 1; z += 2)
{
casterBoundVerts[i++] = bounds.center + Vector3.Scale(bounds.extents, new Vector3(x, y, z));
}
}
}
var debug = camera.name == "Main Camera" && settings.debug;
if (settings.light.type == LightType.Point)
{
//朝向 + shadow框
var rotation = Matrix4x4.Rotate(Quaternion.FromToRotation(Vector3.forward,
settings.transform.worldToLocalMatrix.MultiplyPoint(bounds.center).normalized));
var rotatedView = rotation.inverse * settings.light.transform.worldToLocalMatrix;
var frustumCaster = BestfitFrustum(false, rotatedView, casterBoundVerts);
if (debug)
{
ShadowUtils.DrawBound(bounds, Color.cyan);
ShadowUtils.DrawFrustum(frustumCaster, false, rotatedView.inverse);
}
return(Matrix4x4.Scale(new Vector3(1, 1, -1)) * rotatedView, Matrix4x4.Frustum(frustumCaster));
}
else if (settings.light.type == LightType.Spot)
{
Matrix4x4 lightView = settings.light.transform.worldToLocalMatrix;
var frustumCamera = BestfitFrustum(false, lightView, p0, p1, p2, p3, p4);
var frustumCaster = BestfitFrustum(false, lightView, casterBoundVerts);
var near = settings.nearDistance;
var far = Mathf.Min(frustumCaster.zFar, frustumCamera.zFar, settings.light.range);
return(view, Matrix4x4.Perspective(settings.light.spotAngle, 1, near, far));
}
else if (settings.light.type == LightType.Directional)
{
//shadow框和摄像机框 比较 选择最大/小的
var frustumCamera =
BestfitFrustum(true, settings.light.transform.worldToLocalMatrix, p0, p1, p2, p3, p4);
var frustumCaster = BestfitFrustum(true, settings.light.transform.worldToLocalMatrix, casterBoundVerts);
var left = Mathf.Max(frustumCaster.left, frustumCamera.left);
var right = Mathf.Min(frustumCaster.right, frustumCamera.right);
var bottom = Mathf.Max(frustumCaster.bottom, frustumCamera.bottom);
var top = Mathf.Min(frustumCaster.top, frustumCamera.top);
var zNear = frustumCaster.zNear;
var zFar = Mathf.Min(frustumCaster.zFar, frustumCamera.zFar);
if (debug)
{
var bound = new Bounds();
bound.min = new Vector3(left, bottom, zNear);
bound.max = new Vector3(right, top, zFar);
ShadowUtils.DrawFrustum(new FrustumPlanes()
{
left = Mathf.Max(frustumCaster.left, frustumCamera.left),
right = Mathf.Min(frustumCaster.right, frustumCamera.right),
bottom = Mathf.Max(frustumCaster.bottom, frustumCamera.bottom),
top = Mathf.Min(frustumCaster.top, frustumCamera.top),
zNear = frustumCaster.zNear,
zFar = Mathf.Min(frustumCaster.zFar, frustumCamera.zFar),
}, true, settings.transform.localToWorldMatrix);
//DrawBound(bounds, Color.cyan);
Debug.DrawRay(
settings.transform.localToWorldMatrix.MultiplyPoint(new Vector3(bound.center.x, bound.center.y,
zNear)), settings.transform.forward * 5, Color.green);
}
return(view, Matrix4x4.Ortho(left, right, bottom, top, zNear, zFar));
}
return(Matrix4x4.identity, Matrix4x4.identity);
}
