ray tracing tutorial. ray casting one type of visibility algorithm

Ray Tracing Tutorial

Ray CastingOne type of visibility algorithm

Basic IdeaRayCast(Camera, Scene, img_w, img_h)

{

for (row=0; row < img_h; row++) {

for (col=0; col< img_h; col++) {

ray = constructRay(camera, row, col);

(hit,color)=getIntersection(ray, scene);

image[row][col] = color;

}

}

return image

}

Constructing Primary Rays

CoP

u

nv

Xmin, Ymin

Constructing Primary Rays

CoP

Constructing Primary Rays

CoP

Constructing Primary Rays

CoP

Gathering all the info from .dat file

Camera specification

• Viewport <width> <height>

• Resolution <x_res> <y_res>

• Camera {perspective, orthographic}

<cop_x><cop_y><cop_z>

<look_x><look_y><look_z>

<up_z><up_y><up_z>

<focal_length>

<near_plane> <far_plane>

CoP point

lookat point

up vector

Visualizing the components

CoP

Look at point

up vector

Width (in pixels)

Height (in pixels)

x_res

y_res

focal length

Constructing the Orthogonal Basis

CoP

Look at point

up vector

u

n

v

n = normalize lookat vector u = n x upv = u x n

Computing Starting Point

CoPu

n

v

X, Y

Beware of units. Pixels versus world units

focal length

Constructing a Primary Ray

CoP

CoP

Cast Ray

Current Pixel Color(0.2,0.8,0.2) due to ambientterm

CoP

Check for Intersections

Current Pixel Color(0.2,0.8,0.2) due to ambientterm

Beware of near and farclipping planes as well

Some Tips• Try the simplest test case you can think of

(eg one sphere, and simple camera location)

• Break Down into steps– Ray Cast in BW with spheres (ensure

generation of primary rays is correct)– Shade with Primary Ray contribution.– Try more complex surfaces

• Normalize, Normalize, Normalize

• Clamp color [0,1]

CoP

Pick Nearest

Current Pixel Color(0.2,0.8,0.2) due to ambientterm

Computing the Surface Lighting Effect

CoP

ConnectLight Ray

Current Pixel Color(0.2,0.8,0.2) due to ambientterm

IR = IR,ambdiff + IR,diffused + IR,specular

IG = IG,ambdiff + IG,diffused + IG,specular

IB = IB,ambdiff + IB,diffused + IB,specular

I = Iambdiff + I diffused + I specular

For example (0.2, 0.8, 0.2) for this material.A constant. Independent of lightingAnd viewing direction

I = Iambdiff + I diffused + I specular

N

LIdiffused = kd Il (N.L)

Compute for all 3 channels. For example (0.1, 0.1, 0.1).

Independent of Viewpoint

I = Iambdiff + I diffused + I specular

N

LIspecular = ks Il (V.R)ns

Compute for all 3 channels. For example (0.2, 0.2, 0.2).

V

R

I = Iambdiff + I diffused + I specular

= (0.2, 0.8, 0.2) + (0.1, 0.1, 0.1) + (0.2, 0.2, 0.2)

= (0.5, 1.0, 0.5)

Clamp to [0,1]

CoP

Current Pixel Color(0.5,1.0,0.5)

ConnectLight Ray

What about areas in shadow?

CoP Current Pixel Color(0.2,0.8,0.2) due toAmbient term

ConnectLight Ray

Ray Tracing• Physical World :

– Photons shoot out from light sources, reflect off surfaces and into the eye.

– Problem : Only small fraction reaches the eye (or image plane). Difficult to simulate.

• Alternative way to simulate :– Reverse the process!– Trace the path backwards i.e from the eye (or

pixels) back to the light sources.– Ray Tracing!

We modify the Ray-Casting algorithm to trace rays bouncing

off the surfaces.

Outer Loop

Select center of projection and window on view plane;

For (each scan line in image) {

For (each pixel in scan line) { 1) Construct ray from center of projection through pixel 2) pixel = trace(ray,1);

}

}

color trace(RT_ray ray, int depth) {Determine closest intersection of ray with an object

if there is an intersection {

1) compute normal at intersection

2) return shade ( closest object hit, ray, intersection, normal, depth)

}

}

Shade will return the cumulative color by recursively calling tracewith depth counter decremented at each invocation.

CoP

ContributionFrom PrimaryRay

(0.5,1.0,0.5)

CoP

ContributionFrom SecondaryRay

(0.5,1.0,0.5)

V2

V1

L (0.8,0.8,0.0)

CoP

Final Pixel Color

(0.5,1.0,0.5)

V2

V1

L (0.8,0.8,0.0)+ =ks

The End