Ray Casting: Generating Images by Shooting Rays into a Scene, Slides of Computer Graphics

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• Ray Casting

Programming 3 Info

• Test data for part 1 (Lines) is available
  • As C/C++ array, or just as a text file
    • In both cases, each line has 7 parameters
      • (x 1 , y 1 , x 2 , y 2 , R, G, B)
    • This data set anticipates a 512x512 window
  • To read the array (line.data), use something like the following code:

Programming 3 Info

• For part 3 (line clipping), should display

a window bigger than the clip window

• i.e. Viewport (^) Clip against this

Last Time

• Derived the math for ray casting
  • Intersecting rays and objects
  • Generating rays
    • aka generating a camera matrix
  • Coloring pixels
    • Phong shading for each ray

Ray-Tracing Algorithm

• for each pixel / subpixel

shoot a ray into the scene

find nearest object the ray intersects

if surface is (nonreflecting OR light)

color the pixel

else

calculate new ray direction

recurse

Ray-Tracing Algorithm

• for each pixel / subpixel

shoot a ray into the scene

find nearest object the ray intersects

if surface is (nonreflecting OR light)

color the pixel

else

calculate new ray direction

recurse

Ray Casting

Computing Ray-Object Intersections

• If a ray intersects an object, want to

know the value of t where the

intersection occurs:

• t < 0: Intersection is behing the ray, ignore it
• t = 0: Undefined
• t > 0: Good intersection
• If there are multiple intersections, we

want the one with the smallest t

• This will be the closest surface r (t) = p + t d

Generating Rays

• Now, given a ray, we know how to test if it

intersects an object

• But we don’t yet know how to generate the rays
• We talked a bit about lenses last time, but

an ideal pinhole camera is still the simplest

model

• So let’s assume that

Generating Rays in 2D

Eye Once we know this ray, the rest are easy This is referred to as a “Pencil of Rays”

Generating Rays in 3D

Eye +x +y +z

D v =

D u =

V 0 D v D u V 0 =

A Basic 3D Camera Matrix

• Assumes:
  • Camera on the z-axis
  • Looking down - z
  • Ideal pinhole model
  • Fixed focal length (focal length = 1)

Determining Color

• Since we’re not yet talking about tracing

rays

• Really just talking about OpenGL-style lighting and shading - Since surfaces are implicitly defined, can solve Phong lighting equation at every intersection

Camera Intrinsics and Extrinsics

• We normally divide camera properties

into two classes: intrinsic and

extrinsic

• Intrinsic properties are those belonging to the camera itself - Intrinsic properties are inside the camera
• Extrinsic properties define how the camera is situated in the world

Camera Intrinsics

• These describe the behavior of the camera
  • Focal length
  • Aspect ratio
  • Resolution
  • Aperture
  • Shutter speed
  • etc.