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Member Since 15 Sep 2006
Offline Last Active Aug 19 2013 12:10 PM

Topics I've Started

Stable Cascaded Shadow Maps have made me lose all my hair

17 July 2013 - 10:01 PM

I've been working furiously and so far stable cascaded shadow maps are mocking me..... I can't seem to get this working for the life of me.....


So I will run through my algorithm and perhaps some kind soul will take pity on me and show me the error of my ways......


[1] I calculate the split frustum values for FOUR cascades.


     I use this equation:

    // get the currently active camera
    ICamera *pcCamera = getCurrentCamera ();
    vsAssert (pcCamera != NULL);

    if (m_fSplitNearZ < pcCamera->getNearZ ())
        m_fSplitNearZ = pcCamera->getNearZ ();


    for (vsInt32 iSplit = 1; iSplit < NUM_CASCADE_SPLITS; iSplit++)
        vsFloat32 fStep = iSplit / (vsFloat32) NUM_CASCADE_SPLITS;

        vsFloat32 fLogSplit = m_fSplitNearZ * powf (m_fSplitFarZ / m_fSplitNearZ, fStep);

        vsFloat32 fLinearSplit = m_fSplitNearZ + (m_fSplitFarZ - m_fSplitNearZ) * fStep;

        // linearly interpolate between the linear and logarithmic split values
        m_fSplitPositions [iSplit] = fLogSplit * m_fLogSplitWeight + fLinearSplit * (1.0f - m_fLogSplitWeight);

    // ensure the border split values are accurate
    m_fSplitPositions [0] = m_fSplitNearZ;
    m_fSplitPositions [NUM_CASCADE_SPLITS] = m_fSplitFarZ;

So now I have my frustum splits.....


I use these splits to calculate the corners of the cascade frustum that is being considered. So if I am going to update the first cascade shadow map I use the first and second frustum split positions. ie. m_fSplitPositions [0] and m_fSplitPositions [1].


So now I have 8 view space corners for the split frustum in view space. I generate the bounding box of these points and get the center. Again this is in View space. I take the max AABB point, subtract from the centroid I calculated and get it's length. This is what I use as the radius of the sphere that encloses this split frustum.


I then multiply the View Space frustum center by the inverse view to get the center in world space. I do the above for all FOUR cascade frustums when I am done I have FOUR spheres in TOTAL. One for each split sub frustum. Since I have 4 cascades I have 4 spheres.

CalculateCascadeBoundingSphere (void)
    // find the minimum enclosing sphere for the split frustum, this is done in
    // local space to avoid precision variation between frames

    ICamera *pcCurrentCamera = getCurrentCamera ();
    vsAssert (pcCurrentCamera != NULL);

    vsFloat32 fTanHalfFOVY = pcCurrentCamera->getTanHalfFOVY ();
    vsFloat32 fTanHalfFOVX = fTanHalfFOVY * pcCurrentCamera->getAspectRatio ();

    vsFloat32 fNearX = fTanHalfFOVX * m_fCurrentNearSplit;
    vsFloat32 fNearY = fTanHalfFOVY * m_fCurrentNearSplit;
    vsFloat32 fNearZ = m_fCurrentNearSplit;

     vsFloat32 fFarX = fTanHalfFOVX  * m_fCurrentFarSplit;
     vsFloat32 fFarY = fTanHalfFOVY * m_fCurrentFarSplit;
     vsFloat32 fFarZ = m_fCurrentFarSplit;

    // calculate the frustum AABB in view space
    CAABB cFrustumAABB;

    cFrustumAABB.m_cMin.setVector (FLT_MAX, FLT_MAX, FLT_MAX);
    cFrustumAABB.m_cMax.setVector (-FLT_MAX, -FLT_MAX, -FLT_MAX);

    cFrustumAABB.Add (CVector3 (fNearX, fNearY, fNearZ));
    cFrustumAABB.Add (CVector3 (fNearX, -fNearY, fNearZ));
    cFrustumAABB.Add (CVector3 (-fNearX, -fNearY, fNearZ));
    cFrustumAABB.Add (CVector3 (-fNearX, fNearY, fNearZ));

    cFrustumAABB.Add (CVector3 (fFarX, fFarY, fFarZ));
    cFrustumAABB.Add (CVector3 (fFarX, -fFarY, fFarZ));
    cFrustumAABB.Add (CVector3 (-fFarX, -fFarY, fFarZ));
    cFrustumAABB.Add (CVector3 (-fFarX, fFarY, fFarZ));

    CVector3 cCenter, cRadius;

    cCenter.Add (cFrustumAABB.m_cMin, cFrustumAABB.m_cMax);
    cCenter.MulScalar (0.5f);

    cRadius.Sub (cFrustumAABB.m_cMax, cCenter);

    vsFloat32 fRadius = cRadius.getLength ();

These spheres I use to generate FOUR light view and FOUR light view projection matrices. I do that as follows:


Remember I do this FOUR times, so at the end I have FOUR light view matrices and FOUR light projection matrices:

CalculateCascadeViewMatrix (vsUInt32 iCascade)
    vsAssert (m_pcDirectionalLightEditorObject != NULL);

    // calculate the cascade view matrix

    const CVector3 &rcLightDirection = m_pcDirectionalLightEditorObject->getDirection ();

    CVector3 cEye, cTarget;

    // target is center of view split frustum in world space
    cTarget.setVector (m_cCurrentCascadeBoundingSphere [iCascade].m_cCenter);

    // scale the light direction based on the shadow range
    CVector3 cScaledLightDirection (rcLightDirection);
    cScaledLightDirection.MulScalar (m_fShadowRange);

    // eye = target - (light_direction * shadow_range)
    cEye.Sub (cTarget, cScaledLightDirection);

    // generate the light view look at matrix
    LookAt (m_cViewMatrix [m_iCascade], cEye, cTarget);

LookAt (CMatrix4 &rcViewMatrix, const CVector3 &rcEye, const CVector3 &rcTarget)
    CVector3 cZAxis;

    // we look down -z axis this is why vector is reversed
    cZAxis.Sub (rcEye, rcTarget);
    cZAxis.Normalize ();

    CVector3 cYAxis (CVector3::Y_AXIS);

	// check it's not coincident with direction
    if (CMath::FAbs (cYAxis.DotProduct (cZAxis)) >= 1.0f)
	  // use camera up
          cYAxis.setVector (CVector3::Z_AXIS);

    // cross twice to rederive, only direction is unaltered
    CVector3 cXAxis;
    cXAxis.CrossProduct (cYAxis, cZAxis);
    cXAxis.Normalize ();

    cYAxis.CrossProduct (cZAxis, cXAxis);
    cYAxis.Normalize ();

    // setup the light view matrix (this places objects in light view space)
    rcViewMatrix.m [m00] = cXAxis.x;
    rcViewMatrix.m [m01] = cXAxis.y;
    rcViewMatrix.m [m02] = cXAxis.z;
    rcViewMatrix.m [m03] = -cXAxis.DotProduct (rcEye);

    rcViewMatrix.m [m10] = cYAxis.x;
    rcViewMatrix.m [m11] = cYAxis.y;
    rcViewMatrix.m [m12] = cYAxis.z;
    rcViewMatrix.m [m13] = -cYAxis.DotProduct (rcEye);

    rcViewMatrix.m [m20] = cZAxis.x;
    rcViewMatrix.m [m21] = cZAxis.y;
    rcViewMatrix.m [m22] = cZAxis.z;
    rcViewMatrix.m [m23] = -cZAxis.DotProduct (rcEye);

    rcViewMatrix.m [m30] = 0.0f;
    rcViewMatrix.m [m31] = 0.0f;
    rcViewMatrix.m [m32] = 0.0f;
    rcViewMatrix.m [m33] = 1.0f;

Ok now I generate FOUR orthographic projection matrices, using the radius values of the four frustum split bounding spheres I generated up above:

CalculateCascadeProjectionMatrix (vsUInt32 iCascade)
    vsFloat32 fWidth = m_cCascadeBoundingSphere [iCascade].m_fRadius * 2.0f;
    vsFloat32 fHeight = m_cCascadeBoundingSphere [iCascade].m_fRadius * 2.0f;

    // calculate the cascade orthographic projection matrix
    m_cProjectionMatrix [iCascade].m [m00] = 2.0f / fWidth;
    m_cProjectionMatrix [iCascade].m [m11] = 2.0f / fHeight;

    m_cProjectionMatrix [iCascade].m [m22] = -2.0f / (m_fProjectionFarZ - m_fProjectionNearZ);
    m_cProjectionMatrix [iCascade].m [m23] = -(m_fProjectionFarZ + m_fProjectionNearZ) / (m_fProjectionFarZ - m_fProjectionNearZ);
    m_cProjectionMatrix [iCascade].m [m33] = 1.0f;

    // engine specific projection matrix with render system depth range
    m_pcRenderSystem->ConvertProjectionMatrix (m_cProjectionMatrix [iCascade], m_cProjectionRSDepthMatrix [iCascade], true);

I also generate a rounding matrix to prevent the shadow map cascades from shimmering as the camera translates:

CalculateCascadeRoundMatrix (vsUInt32 iCascade)
    CVector3 cOriginShadow;
    CVector3 cOrigin (0.0f, 0.0f, 0.0f);

    // transform origin to light view projection space
    m_cLightViewProjectionMatrix [iCascade].Transform (cOriginShadow, cOrigin);

    vsFloat32 fShadowMapSize = getShadowMapSize ();

    // convert clip space to texture coordinates
    vsFloat32 fTexCoordX = cOriginShadow.x * fShadowMapSize * 0.5f;
    vsFloat32 fTexCoordY = cOriginShadow.y * fShadowMapSize * 0.5f;

    // round to the nearest whole texel
    vsFloat32 fTexCoordRoundedX = CMath::Round (fTexCoordX);
    vsFloat32 fTexCoordRoundedY = CMath::Round (fTexCoordY);

       the difference between the rounded and actual tex coordinate is the
       amount by which we need to translate the shadow matrix in order to
       cancel sub-texel movement
    vsFloat32 fDX = fTexCoordRoundedX - fTexCoordX;
    vsFloat32 fDY = fTexCoordRoundedY - fTexCoordY;

    // transform fDX, fDY back to homogenous light space
    fDX /= fShadowMapSize * 0.5f;
    fDY /= fShadowMapSize * 0.5f;

    // set the rounding matrix
    m_cRoundMatrix [iCascade].m [m03] = fDX;
    m_cRoundMatrix [iCascade].m [m13] = fDY;
    m_cRoundMatrix [iCascade].m [m23] = 0.0f;
    m_cRoundMatrix [iCascade].m [m33] = 1.0f;

So now I have CMatrix4x4 m_cLightViewMatrix [4],  CMatrix4x4 m_cLightProjectionMatrix [4] and m_cRoundMatrix [4];


I loop like so and generate the shadow matrix:


for (iCascade = 0; iCascade < 4; iCascade++)


       m_cShadowMatrix [iCascade] = m_cRoundMatrix [iCascade] * m_cLightProjectionMatrix [iCascade] * m_cLightViewMatrix [iCascade];



I use m_cShadowMatrix [4] to generate the shadow maps in my shadow atlas..... So In the shader I generate the vertices of the shadow caster into word space and then multiply like so:


         m_cShadowMatrix * m_cWorldMatrix * vsInput.vPosition;


In the pixel shader I save out the z value.


Is my algortihm sound? Or perhaps I missed something in my understanding of the algorithm. I would appreciate any help anyone can give me as to where I could be going wrong. Also if anyone knows of any demos with source that I could run to test this algorithm I would be ever so greatful.


Many thanks to anyone who can help me!

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