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OpenGL Directional light shadow mapping

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I am doing cascaded shadowmapping and having some issues.

 

I have a scene like this (yellow light is from a point light; theres also a chair just outside the view to the left):

 

[attachment=26364:1.png]

 

If do not use a lights view matrix at all, i.e I only use an orthographic projection matrix when rendering shadow maps, it looks OK. The cascade order is top left, top right, bottom left, bottom right.

 

[attachment=26365:asd.png]

 

Now if I use an orthographic projection matrix and use a rotation matrix (as in the code below) based on the lights direction, it instead looks like this:

 

[attachment=26366:asd2.png]

 

Which is not correct, for example, the boxes are completely missing, even though they are encompassed in the orthographic projection

 

The resulting shadows then look like this:

 

[attachment=26369:asd3.png]

 

Some parts of shadow are correct, but major artifacts.

 

Here's how I build the matrix:

Mat4 CreateDirLightVPMatrix(const CameraFrustrum& cameraFrustrum, const Vec3& lightDir /* == Vec3(-1.0f, -1.0f, -1.0f) in this example */)
{
	// "cameraFrustrum" contains the 8 corners of the cameras frustrum in world space
	float maxZ = cameraFrustrum[0].z, minZ = cameraFrustrum[0].z;
	float maxX = cameraFrustrum[0].x, minX = cameraFrustrum[0].x;
	float maxY = cameraFrustrum[0].y, minY = cameraFrustrum[0].y;
	for (uint32_t i = 1; i < 8; i++)
	{
		if (cameraFrustrum[i].z > maxZ) maxZ = cameraFrustrum[i].z;
		if (cameraFrustrum[i].z < minZ) minZ = cameraFrustrum[i].z;
		if (cameraFrustrum[i].x > maxX) maxX = cameraFrustrum[i].x;
		if (cameraFrustrum[i].x < minX) minX = cameraFrustrum[i].x;
		if (cameraFrustrum[i].y > maxY) maxY = cameraFrustrum[i].y;
		if (cameraFrustrum[i].y < minY) minY = cameraFrustrum[i].y;
	}

	Vec3 right = glm::normalize(glm::cross(glm::normalize(lightDir), Vec3(0.0f, 1.0f, 0.0f)));
	Vec3 up = glm::normalize(glm::cross(glm::normalize(lightDir), right));

	Mat4 lightViewMatrix = Mat4(Vec4(right, 0.0f),
								Vec4(-up, 0.0f),		// why do I need to negate this btw?
								Vec4(lightDir, 0.0f),
								Vec4(0.0f, 0.0f, 0.0f, 1.0f));

	return OrthographicMatrix(minX, maxX, maxY, minY, maxZ, minZ) * lightViewMatrix;
}

It was my understanding (based on topics like https://www.opengl.org/discussion_boards/showthread.php/155674-Shadow-maps-for-infinite-light-sources), that all I needed to do shadow mapping for directional light was an orthographic projection matrix and then a rotation matrix (with no translation component, since the dir light has no position, and as I've understod it, translation dosnt matter since it is orthographic meaning no perspective anyway).

 

Then what is causing the errors in the 3rd image? Is there something I am missing?

Edited by KaiserJohan

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Which is not correct, for example, the boxes are completely missing, even though they are encompassed in the orthographic projection

So how are you culling them?


L. Spiro

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If you want your camera to move past it's original position, then you'll need a light matrix to do a transform. The directional light has no position, but your orthographic projection still needs to know where it's pointing at and what it's bounds are.

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Which is not correct, for example, the boxes are completely missing, even though they are encompassed in the orthographic projection

So how are you culling them?


L. Spiro

 

 

Not sure I follow; they are in the bounds of the orthographic matrix (as seen in the 2nd image) so why are they not visible after I apply the rotation matrix?

 

If you want your camera to move past it's original position, then you'll need a light matrix to do a transform. 

 

What has this got to do with the (scene) camera? Or do you mean the camera as in the lights view? If so, my understanding of orthographic projection was that I didn't need to translate the camera at all

 

 

 

The directional light has no position, but your orthographic projection still needs to know where it's pointing at and what it's bounds are.

 

"Where its pointing at" - defined by the rotation matrix? "What its bounds are" - defined by the orthographic projection matrix, built from the max/min of the camera frustrum corners? Is there anything I'm missing?

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so why are they not visible after I apply the rotation matrix?

I guess that was my point.
Why isn’t it visible? How are you culling it? How are you drawing it?
Are you sure it is in view? Because if so, and you actually sent valid commands to draw it, it would be there with the rest of the objects.


L. Spiro

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so why are they not visible after I apply the rotation matrix?

I guess that was my point.
Why isn’t it visible? How are you culling it? How are you drawing it?
Are you sure it is in view? Because if so, and you actually sent valid commands to draw it, it would be there with the rest of the objects.


L. Spiro

 

 

I'm positive the problem is related to the projection and/or lights view matrix. Is there anything I'm missing when building the lights projection/view matrix? It is true the view matrix needs no translation at all and just the rotation as in my code above?

Edited by KaiserJohan

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It is true the view matrix needs no translation at all and just the rotation as in my code above?

 

False. The projection determines the size and shape of a frustum "box." That box has no direct relationship to world coordinates. The view matrix determines the position and orientation of objects that will (eventually) be included/excluded from the frustum volume. Thinking in sort a backwards sense, the view matrix "positions" the frustum volume in the world, and objects which are not in the volume don't get rendered.

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It is true the view matrix needs no translation at all and just the rotation as in my code above?

 

False. The projection determines the size and shape of a frustum "box." That box has no direct relationship to world coordinates. The view matrix determines the position and orientation of objects that will (eventually) be included/excluded from the frustum volume. Thinking in sort a backwards sense, the view matrix "positions" the frustum volume in the world, and objects which are not in the volume don't get rendered.

 

 

That makes sense!

So, if I already have the world position of the box, how do I build a view matrix that dosn't change the position, only the orientation of the objects?

I.e, I have the world space corners of the camera frustrum, that will build the ortho box. I want the objects in it, but viewed from a certain direction, how do I build such a matrix? 

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MJP has a good sample on how to do that here: https://mynameismjp.wordpress.com/2009/02/17/deferred-cascaded-shadow-maps/.

Essentially you make an AABB around the game camera, find the center of the box, project a point from that position in the opposite direction of your light's direction scaled by some factor. The scale factor determines how far your light pos will be from the camera, the closer you are the better resolution you'll get in your shadow map, but you may cull valid occluders since they are behind the camera or such. There is a lot of fiddling with that value to get it right, in my experience.

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First (minor) thing is you should normalize your lightDir as well. And your lightView matrix is actually a lookAt matrix.

 

I've implemented a 1-cascade shadow map, the solution is very similar. This is based on an nvidia paper and other resources which can be found in the internet. smile.png

 

So the first step, I calculate a view matrix like you do. This is actually the same as your code (just normalize your direction! smile.png)

view.lookAt(Vector3::Zero, lightDir, Vector3::Up);

After I calculate the bounds of the view frustum points "looked from the direction of the light"

Vector3 min = Vector3::Max;
Vector3 max = Vector3::Min;

for (int i = 0; i < BoundingFrustum::NumCorners; i++)
{
    transformed = Vector3::transformCoord(corners[i], view);

    min = Vector3::getMin(transformed, min);
    max = Vector3::getMax(transformed, max);
}

Then my projection matrix is a simple ortho:

proj.orthographicOffCenter(-1, 1, -1, 1, min.z, max.z);

But I'm using another matrix called cropMat which will "position and clip".

const float32 scaleX = 2.0f / (max.x - min.x);
const float32 scaleY = 2.0f / (max.y - min.y);
const float32 offsetX = -0.5f * (min.x + max.x) * scaleX;
const float32 offsetY = -0.5f * (min.y + max.y) * scaleY;

cropMat.m00 = scaleX;
cropMat.m11 = scaleY;
cropMat.m22 = 1.0f;
cropMat.m30 = offsetX;
cropMat.m31 = offsetY;
cropMat.m33 = 1.0f;

The final viewProj matrix is calculated by multiplying the view, the projection and the crop matrix. NOTE that I'm using the DX-based matrices, care with the matrix row/column order. smile.png

 

As a side note:

You can use a sphere instead of a box. With a sphere you loose some precision but it also disables the flickering when the camera rotates:

Vector3 center;
for (int i = 0; i < BoundingFrustum::NumCorners; i++)
    center += corners[i];
center /= BoundingFrustum::NumCorners;
center = Vector3::transformCoord(center, view);

const float32 radius = Vector3::distance(corners[BoundingFrustum::FLB], corners[BoundingFrustum::NRT]);

min = center - Vector3(radius);
max = center + Vector3(radius);

You can also apply a rounding matrix which disables flickering when camera moves, something like this:

// round to textel
Vector3 origin = Vector3::transformCoord(Vector3::Zero, viewProj);
origin *= halfSize;

Vector3 rounding;
rounding.x = Math::round(origin.x) - origin.x;
rounding.y = Math::round(origin.y) - origin.y;
rounding /= halfSize;

roundMat.translate(rounding);
viewProj *= roundMat;

 

Edit:
This is an old code, can contains bugs. :)

Edited by csisy

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      creates a special rotation-translation matrix that moves and rotates the grid away from the origin so that when i finally
      normalize all the vertices on my vertex shader i can get a perfect sphere.
      T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, 1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(180.0), glm::dvec3(1.0, 0.0, 0.0)); sides[0] = new TerrainNode(1.0, radius, T * R, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_FRONT)); T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, -1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(0.0), glm::dvec3(1.0, 0.0, 0.0)); sides[1] = new TerrainNode(1.0, radius, R * T, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_BACK)); // So on and so forth for the rest of the sides As you can see, for the front side grid, i rotate it 180 degrees to make it face the camera and push it towards the eye;
      the back side is handled almost the same way only that i don't need to rotate it but simply push it away from the eye.
      The same technique is applied for the rest of the faces (obviously, with the proper rotations / translations).
      The matrix that result from the multiplication of R and T (in that particular order) is send to my vertex shader as `r_Grid'.
      // spherify vec3 V = normalize((r_Grid * vec4(r_Vertex, 1.0)).xyz); gl_Position = r_ModelViewProjection * vec4(V, 1.0); The `r_ModelViewProjection' matrix is generated on the CPU in this manner.
      // No the most efficient way, but it works. glm::dmat4 Camera::getMatrix() { // Create the view matrix // Roll, Yaw and Pitch are all quaternions. glm::dmat4 View = glm::toMat4(Roll) * glm::toMat4(Pitch) * glm::toMat4(Yaw); // The model matrix is generated by translating in the oposite direction of the camera. glm::dmat4 Model = glm::translate(glm::dmat4(1.0), -Position); // Projection = glm::perspective(fovY, aspect, zNear, zFar); // zNear = 0.1, zFar = 1.0995116e12 return Projection * View * Model; } I managed to get rid of z-fighting by using a technique called Logarithmic Depth Buffer described in this article; it works amazingly well, no z-fighting at all, at least not visible.
      Each frame i'm rendering each node by sending the generated matrices this way.
      // set the r_ModelViewProjection uniform // Sneak in the mRadiusMatrix which is a matrix that contains the radius of my planet. Shader::setUniform(0, Camera::getInstance()->getMatrix() * mRadiusMatrix); // set the r_Grid matrix uniform i created earlier. Shader::setUniform(1, r_Grid); grid->render(); My planet's radius is around 6400000.0 units, absurdly large, but that's what i really want to achieve;
      Everything works well, the node's split and merge as you'd expect, however whenever i get close to the surface
      of the planet the rounding errors start to kick in giving me that lovely stairs effect.
      I've read that if i could render each grid relative to the camera i could get better precision on the surface, effectively
      getting rid of those rounding errors.
       
      My question is how can i achieve this relative to camera rendering in my scenario here?
      I know that i have to do most of the work on the CPU with double, and that's exactly what i'm doing.
      I only use double on the CPU side where i also do most of the matrix multiplications.
      As you can see from my vertex shader i only do the usual r_ModelViewProjection * (some vertex coords).
       
      Thank you for your suggestions!
       
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