Depth

Depth Cues

"Hints" that suggest three-dimensionality - shape or distance

Based on physics, and workings of human vision

Summary

occlusion
linear perspective
relative size
relative height
texture gradient
shading, shadows
aerial perspective
accomodation
stereo parallax
motion parallax

Occlusion / Interposition

Limbourg. Tres Riches Heures: January. 1412-16

Occlusion / Interposition

Hiroshige. Plum Estate, Kameido. 1857

Occlusion / Interposition

Diablo

Perspective

Linear Perspective
Relative Size
Relative Height
Texture Gradient

Linear Perspective

van Gogh. Corridor in the Asylum. 1889

Linear Perspective

Dali. The First Days of Spring 1932

Linear Perspective

Tempest

Relative Size

Durer. The Adoration of the Magi. 1504

Relative Size

Monet. Wheatstacks (End of Summer), 1890-91

Relative Size

Wolfenstein 3D

Relative Height

Limbourg. Tres Riches Heures: February. 1412-16

Relative Height

Constable. Chain Pier, Brighton. 1827

Relative Height

Marble Madness

Texture Gradient

Botticelli. The Birth of Venus. c. 1485-86

Texture Gradient

Hockney. A Lawn Being Sprinkled. 1967

Texture Gradient

Hockney. A Lawn Being Sprinkled (detail)

Texture Gradient

Lighting & Shadows

Michelangelo. David. 1504

Lighting & Shadows

Michelangelo. The Holy Family with the infant St. John the Baptist (the Doni Tondo). c. 1503-05

Lighting & Shadows

Monet. Rouen Cathedral, the West Portal and Saint-Romain Tower, Full Sunlight, Harmony in Blue and Gold) / Rouen Cathedral: Full Sunlight. 1894

Lighting & Shadows

Mario 64 / Doom 3

Aerial Perspective

Friedrich. Riesengebirge. 1835

Aerial Perspective

Monet. The Thames at Westminster (Westminster Bridge). 1871

Aerial Perspective

Grand Theft Auto 3

Accomodation (Focus)

Vermeer. The Lacemaker. 1669-70

Accomodation (Focus)

Wyler. The Little Foxes. 1941

Accomodation (Focus)

Motion Parallax

Disner. The Old Mill. 1937

Motion Parallax

Shadow of the Beast

Stereo Parallax

Virtual Boy - Mario's Tennis

OpenGL

occlusion: depth-buffering (glEnable(GL_DEPTH_TEST))
linear perspective
relative size
relative height: perspective projection (gluPerspective)
texture gradient: perspective, texture mapping (glTexImage2D, etc)
shading, shadows: lighting (glLight, glMaterial, glNormal)
aerial perspective: fog (glFog)
accomodation: accumulation buffer (glAccum)
stereo parallax: quad-buffering, color-masking
motion parallax: transformations

Hidden Surfaces

Hidden surfaces provide occlusion depth cue

Hidden Surface Algorithms

Many different algorithms developed over the years

Painter's algorithm
- sort everything from back to front
Binary Space Partition (BSP) tree
Ray casting / Ray tracing
Depth buffering
(aka Z buffering)
etc

Ray Tracing

For each pixel, compute a ray backwards from the eye through the pixel
Test for intersection with any objects
Trace rays from intersection point to light sources
Check for occlusion of rays to lights (shadows)

Depth Buffering

Rendering a polygon means filling pixels

Color buffer contains RGB color of each pixel drawn

Depth buffer contains depth of each pixel drawn

Color	Depth

Depth Buffer

When drawing a new pixel, compare new depth to what's stored in depth buffer

Color	Depth

Polygons can be drawn in any order
Polygons can intersect

OpenGL Depth Buffering

Space must be allocated for the depth buffer:

glutInitDisplayMode(GLUT_RGB|GLUT_DOUBLE|GLUT_DEPTH)

Depth buffering must be enabled:

glEnable(GL_DEPTH_TEST)

Depth buffer must be cleared each frame:

glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

Depth Fighting

Depth values have limited resolution

i.e. the numbers are not infinitely precise

Rounding errors occur when polygons are filled

Polygon overlap can cause "depth-fighting"

Perspective Projection

Perspective effects are created by a perspective projection transformation

Linear perspective
Relative size
Relative height
Texture gradient

Perspective + movement also yields motion parallax

Orthographic Projection

Orthographic projection : projects rectilinear box onto display
Objects will not appear to change size with distance

Perspective Projection

Perspective projection : projects frustum (truncated pyramid) onto disp lay
Near objects appear larger, distant objects appear smaller

Perspective Projection

GL's perspective projection is, conceptually, a pin-hole camera, located at origin, looking down -Z axis

Camera has a field-of-view - angle representing (horizontal) extent of region viewed

Small angle = narrow field-of-view = telephoto lens
Large angle = wide field-of-view = wide-angle lens

OpenGL Perspective

    gluPerspective( fovy, aspect, zNear, zFar )

fovy = field of view, in Y direction, in degrees

aspect = aspect ratio (X:Y) of window

zNear = distance to near clipping plane

zFar = distance to far clipping plane

The "eye-point" of the perspective projection is at (0,0,0)

Example:

    gluPerspective(45, 1.333, 0.1, 100)

This document is by Dave Pape, and is released under a Creative Commons License.