Lesson 2 – Shadows
PV227 – GPU Rendering
Jiˇrí Chmelík, Jan ˇCejka
Fakulta informatiky Masarykovy univerzity
24. 09. 2019
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Shadow mapping
Motivation:
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Shadow mapping
Lance Williams, 1978, Casting curved shadows on curved surfaces
Illustration from NVIDIA: Cg Tutorial.
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Shadow mapping
Individual steps:
Allocate shadow texture, create a framebuffer object.
Render the whole scene from the position of light into the shadow
texture.
Render the whole scene again, now from the position of the
viewer. When rendering each object, use the shadow texture and
compare the depths.
Let’s add shadows to project Cv2 (in Study materials).
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Task: Render from the position of the light
Let’s split this task to ease debugging:
Task 1
Compute and update projection and view matrices for rendering
from the position of the light.
Render from the position of the light.
Render into the main window.
Use the same shaders that are used when rendering from the
viewer.
Do not render the object that represents the light.
Hint: Use function glm::perspective to create the projection matrix.
Hint: Use function glm::lookAt to create the view matrix.
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Task: Render from the position of the light
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Task: Render from the position of the light
Task 2
Render the scene into the shadow map instead (using the same
shaders as before).
Display the shadow map on the screen.
Task 3 (Optional)
Prepare and use simplified shaders for rendering into the shadow
texture, i.e. don’t compute the lighting, don’t use textures, don’t use
materials, don’t output any color.
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Task: Render from the position of the light
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Theory: Transformations and depth
Normalized device coordinates, from songho.co
Vndc = DivideByW(proj ∗ view ∗ Vworld )
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Theory: Transformations and depth
Vndc ∈ (−1, −1, −1); (1, 1, 1)
After applying glViewport and glDepthRange:
Vscreen ∈ (x, y, near); (x + w, y + h, far)
This Vscreen.z is used for depth tests, stored into the depth buffer etc.
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Theory: Transformations and depth
Texture coordinate?
Reference value to compare?
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Theory: Transformations and depth
Transform inData.position_ws (= Vworld )
V
light
ndc = DivideByW(projlight
∗ viewlight
∗ Vworld )
V
light
ndc ∈ (−1, −1, −1); (1, 1, 1)
Then use transformation and scale
V = T/S ∗ V
light
ndc
V ∈ (0, 0, 0); (1, 1, 1)
Here, V.xy is the texture coordinate, V.z is the reference value
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Theory: Transformations and depth
Transform inData.position_ws (= Vworld )
V
light
ndc = DivideByW(projlight
∗ viewlight
∗ Vworld )
V
light
ndc ∈ (−1, −1, −1); (1, 1, 1)
Then use transformation and scale
V = T/S ∗ V
light
ndc
V ∈ (0, 0, 0); (1, 1, 1)
Here, V.xy is the texture coordinate, V.z is the reference value
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Theory: Transformations and depth
Furthermore:
V = T/S ∗ DivideByW(projlight
∗ viewlight
∗ Vworld )
is actually the same as:
V = DivideByW(T/S ∗ projlight
∗ viewlight
Shadow matrix
∗Vworld )
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Task: Render with shadows
Let’s again split this task to ease debugging:
Task 4
Compute and update shadow matrix, send it into shaders.
Transform inData.position_ws.
Output the reference value V.z as a color in grayscale.
When rendered from the position of the light, this should be the
same as the shadow texture (except for the background).
When rendered from the position of the viewer, the color
corresponds to the distance from the light.
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Task: Render with shadows
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Task: Render with shadows
Task 5
Use the texture coordinates to obtain the value in the shadow
texture.
Display this value as a grayscale color.
When rendered from the position of the light, this should again be
the same as the shadow texture (except for the background).
When rendered from the position of the viewer, the color
corresponds to the closest distance in the shadow map. Since the
closer values correspond to darker colors, this looks like some
sort of shadows.
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Task: Render with shadows
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Task: Render with shadows
Task 6
Compare the reference value and the value in the shadow texture
Apply the result to the lighting.
The result is shadows (and a lot of artefacts).
Hint: Use float to represent the result of the comparison, use 1.0
for “not-in-shadow”, and 0.0 for “in-shadow”.
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Task: Render with shadows
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Artefacts: Acne and Peter-Panning
Shadow Acne
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Artefacts: Acne and Peter-Panning
Shadow Acne:
Objects cast shadows on themselves when they shouldn’t
Caused by quantization of the depth value when stored into the
texture
To fix this issue:
When rendering into the depth texture, use near and far planes as
close to the other as possible.
Offset the depth before storing into the depth texture, preferably by
using glPolygonOffset.
Offset the reference value a bit before comparing it with the value in
the texture (using an additional translation matrix or add a value in
the shader).
When rendering into the depth texture, render only the back faces,
do not render the front faces.
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Artefacts: Acne and Peter-Panning
Don’t overshoot the offset, the object would levitate, creating a
Peter-Panning effect.
Peter-Panning
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Task: Remove the artefacts
Task 7: Choose one of the following to remove the Shadow Acne
artefact:
Add an additional translation matrix to the shadow matrix
Hint: offseting by −0.002 in NDC seems to be OK
Use glPolygonOffset when rendering into shadow texture
Hint: parameters glPolygonOffset(2.0f, 0.0f) seem to be OK
Hint: don’t forget to enable/disable with
glEnable(GL_POLYGON_OFFSET_FILL)
Cull away front faces when rendering into the depth texture
Hint: glEnable(GL_CULL_FACE), glCullFace(GL_FRONT)
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Task: Remove the artefacts
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Other artifacts
Perspective aliasing
Projective aliasing
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Other artifacts
Animation artifacts: Shimmering edges
Images from: Microsoft: Common Techniques to Improve Shadow
Depth Maps
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Techniques improving shadows
Reducing aliasing:
Cascaded Shadow Maps
(Light Space) Perspective Shadow Maps
Smoothing edges:
Percentage Closer Filtering
CSM PSM PCF
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OpenGL support for shadow maps
OpenGL and GLSL provides additional functions for shadow maps:
GLSL function textureProj
divides by w before performing the texture lookup:
texture(shadow_tex, tex_coord.xy / tex_coord.w);
is the same as
textureProj(shadow_tex, tex_coord);
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OpenGL support for shadow maps
Shadow textures
glTexParameteri(..., GL_TEXTURE_COMPARE_MODE, ...)
GL_COMPARE_REF_TO_TEXTURE compares value in texture with
the reference value
GL_NONE no comparison is done
glTexParameteri(..., GL_TEXTURE_COMPARE_FUNC, ...)
GL_LEQUAL comparison returns 1.0 when the reference value is
less or equal that the value in the texture.
Special GLSL sampler sampler2DShadow
float factor = texture(shadow_tex, tex_coord.xyz / tex_coord.w);
is the same as
float factor = textureProj(shadow_tex, tex_coord);
Support for linear filters and mipmapping, which is done after the
comparison.
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Task: Use OpenGL functions
Task 8: Use textureProj and comparison.
Use textureProj.
Use GL_COMPARE_REF_TO_TEXTURE and
sampler2DShadow for shadows.
Use GL_NONE and sampler2D for displaying the shadow texture.
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Foods for thought
Other techniques for shadows:
Stencil shadows
Stencil volume
RayTracing
Shadows for ambient light? (Look up ambient occlusion)
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Foods for thought
How to solve transparent objects? What about semi-transparent
objects? What about colored semi-transparent objects?
What about multiple lights? (Optimization: not all of them needs
shadows.)
What about point lights? What about directional lights like the
sun?
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Further reading
Microsoft: Common Techniques to Improve Shadow Depth Maps
https://msdn.microsoft.com/en-us/library/
windows/desktop/ee416324(v=vs.85).aspx
Microsoft: Cascaded Shadow Maps
https://msdn.microsoft.com/en-us/library/
windows/desktop/ee416307(v=vs.85).aspx
Wikipedia: Shadow mapping, section “Shadow mapping
techniques”
https://en.wikipedia.org/wiki/Shadow_mapping
GPU Gems, GPU Gems 2, GPU Gems 3
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