Nima Kalantari

CSCE 441 - Computer Graphics

​

Shadows

Some slides from Scott Schaefer

Shadows

• Shadows provide clues about depth
• Make scenes appear more realistic

Shadows

• Shadows provide clues about depth
• Make scenes appear more realistic

Outline

• Simple/Planar Shadows
• Shadow Maps
• Shadow Volumes
• Soft shadows

Simple/Planar Shadows

• Projection of an object onto a planar surface (floor/wall)
• Project the object from light to surface
• Draw the projected object with ambient color

Image taken NVIDIA

Simple/Planar Shadows

• Stage 1: Render the scene as usual (there won’t be any shadows)
• Stage 2: project the vertices of objects to the planar surface and draw them only with the ambient color

How to project an object to a planar surface?

Image taken NVIDIA

Ray Equation

Ray is defined by its origin and a direction vector

Plane Equation

Plane is defined by normal vector and a point on plane

Ray Intersection With Plane

How to project an object to a planar surface?

Image taken NVIDIA

Problem

How to project an object to a planar surface?

Image taken NVIDIA

Fixed

Simple/Planar Shadows

Fast and simple

Only for planar surfaces (nothing else has shadows cast on it)

Does not account for self-shadowing

Image taken NVIDIA

Outline

• Simple/Planar Shadows
• Shadow Maps
• Shadow Volumes
• Soft shadows

​

Shadow Maps

Shadow Maps

• Render scene from light’s perspective and save the depth buffer

Shadow Maps

• Render scene from light’s perspective and save the depth buffer

Shadow Map

Shadow Maps

• Render scene from light’s perspective and save the depth buffer
• Render scene from viewer’s

perspective

​

Shadow Maps

• Render scene from light’s perspective and save the depth buffer
• Render scene from viewer’s

perspective

• For every pixel
• Compare depth to the depth value

in shadow map

Shadow Maps

• Render scene from light’s perspective and save the depth buffer
• Render scene from viewer’s

perspective

• For every pixel
• Compare depth to the depth value

in shadow map

Shadow Maps

• Render scene from light’s perspective and save the depth buffer
• Render scene from viewer’s

perspective

• For every pixel
• Compare depth to the depth value

in shadow map

In shadow!

Shadow Maps

• Render scene from light’s perspective and save the depth buffer
• Render scene from viewer’s

perspective

• For every pixel
• Compare depth to the depth value

in shadow map

In shadow!

Shadow Maps

• Render scene from light’s perspective and save the depth buffer
• Render scene from viewer’s

perspective

• For every pixel
• Compare depth to the depth value

in shadow map

Not in shadow!

Shadow Maps

Image taken from http://www.cse.ohio-state.edu/~haleyb/Hardware/ggDepthBuffer.jpg

Shadow map

• Stage 1
• Set up a camera at light
• Render the scene
• Store the depth
• [-1, 1] in NDC
• stored as a texture [0, 1]

Shadow map

• Stage 1
• Set up a camera at light
• Render the scene
• Store the depth
• [-1, 1] in NDC
• stored as a texture [0, 1]

Shadow map

depth

Shadow map

• Stage 2
• Render with viewer camera

​

Shadow map

depth

Shadow map

• Stage 2
• Render with viewer camera
• Project vertices to light camera NDC

Shadow map

depth

xyz in Light NDC

Shadow map

• Stage 2
• Render with viewer camera
• Project vertices to light camera NDC
• Convert the projected vertex from [-1, 1] to [0, 1]

​

Shadow map

depth

xyz between [0, 1]

Shadow map

• Stage 2
• Render with viewer camera
• Project vertices to light camera NDC
• Convert the projected vertex from [-1, 1] to [0, 1]
• Use the xy coordinate to look up the depth in shadow map (z’)
• If z > z’
• In shadow (only ambient)
• Else
• Visible (all shading terms)

​

Shadow map

depth

xyz between [0, 1]

Problem

Shadow map

• Stage 2
• Render with viewer camera
• Project vertices to light camera NDC
• Convert the projected vertex from [-1, 1] to [0, 1]
• Use the xy coordinate to look up the depth in shadow map (z’)
• If z - e > z’
• In shadow (only ambient)
• Else
• Visible (all shading terms)

e is a small number e.g., 0.001

Shadow map

depth

xyz between [0, 1]

Fixed

Problem

Problem

Outside the light

camera view!

Problem

Outside the light

camera view!

z’ = 0

Blue point in shadow!

Hacky solution

• Do not check for shadows if a vertex is outside the view volume of the light camera

​

Correct solution

• Set up 6 cameras at light

​

Shadow Maps

• Advantages
• Simple to implement
• Does not depend on scene complexity
• except to render shadow map
• Proper self-shadowing
• Disadvantages
• Omni-directional light sources require 6 shadow maps to cover every direction
• Fixed resolution image leads to artifacts

​

Shadow Map Resolution

Rendered Image

Shadow Map

Outline

• Simple/Planar Shadows
• Shadow Maps
• Shadow Volumes
• Soft shadows

​

Anatomy of a Shadow

Shadowing�object

Partially

shadowed

object

Light�source

Eye position

(note that shadows are independent of the eye position)

Surface inside�shadow volume

(shadowed)

Surface outside�shadow volume

(illuminated)

Shadow�volume

(infinite extent)

Shadow Volumes

• Build polygons for shadow volumes explicitly
• Render shadow volume polygons from viewer’s

perspective and count inside/outside shadows

​

Image taken from “Practical & Robust Stenciled Shadow Volumes for Hardware-Accelerated Rendering”

Shadow Volumes

Shadowing object

Light�source

Shadow Volumes

Shadowing object

Light�source

Unshadowed�object

Shadow Volume Count = +1+1+1-1-1-1 = 0

Shadow Volumes

Shadowing object

Light�source

Shadowed�object

Shadow Volume Count = +1+1+1-1 = 2

Shadow Volumes

Shadowing object

Light�source

zero

zero

+1

+1

+2

+2

+3

Unshadowed�object

Shadow Volume Count = 0

Implementing Shadow Volumes

• For each surface, find silhouette edges
• Build shadow volume (viewer independent) by extending away from light

​

Image taken from “Practical & Robust Stenciled Shadow Volumes for Hardware-Accelerated Rendering”

Implementing Shadow Volumes

• Render the scene to obtain the depth
• Render shadow volume and keep a buffer for counting faces
• Render front faces and increment if closer than the depth
• Render back faces and decrement if closer than the depth
• If buffer is non-zero, then pixel in shadow

​

Shadow Volumes

Shadowing object

Light�source

Shadowed�object

Shadow Volume Count = +1+1+1-1 = 2

Shadow Volumes: Examples

Image taken from “Doom 3”

Shadow Volumes

• Advantages
• Omni-directional light sources
• Proper self-shadowing behavior
• Pixel perfect shadows

Problems with Shadow Volumes

zero

zero

+1

+1

+2

+2

+3

Unshadowed�object

Shadow Volume Count = +1+1+1-1-1-1 = 0

Problems with Shadow Volumes

zero

zero

+1

+1

+2

+2

+3

Near clip�plane

Far clip�plane

Missed shadow volume intersection due to near clip plane clipping; leads to mistaken count

Unshadowed�object

Shadow Volume Count = +1+1-1-1-1 = -1

Problems with Shadow Volumes

Shadowing object

Light�source

Shadow test fails because

eye in shadow

Shadow Volume Count = 0

Outline

• Simple/Planar Shadows
• Shadow Maps
• Shadow Volumes
• Soft shadows

​

Soft Shadows

• Point lights cause hard shadows
• Lights are not infinitely small points in reality
• Area light sources

cause soft shadows

http://graphics.ucsd.edu/~henrik/images/cbox.html

Soft Shadows

• Point lights cause hard shadows
• Lights are not infinitely small points in reality
• Area light sources

cause soft shadows

http://graphics.ucsd.edu/~henrik/images/cbox.html

Soft Shadows

• Simulate area lights with lots of points lights (Expensive)

​

Image taken from “Practical & Robust Stenciled Shadow Volumes for Hardware-Accelerated Rendering”

The cluster of point lights.

Soft Shadows

• Simulate area lights with lots of points lights
• Blur shadows in image space (cheap, but inaccurate)

http://www.gamedev.net/reference/articles/article2193.asp