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1

Raytracing

COSC 4328/5327

Scott A. King

Render With Triangles COSC4328/5327 Computer Graphics 2

"Villarceau Circles" by Tor Olav Kristensen (2004)

• Flat shading

• Phong Shading

• Now what?

• What lighting effects would we have

trouble

– Shadows (can fake)

– Reflection (can fake)

– Refraction (can fake, but not easily)

– Reflected refraction?

– Harder to fake if moving camera

• So how will we do this?

COSC4328/5327 Computer Graphics 3

Marc Jacquier (2004)


"Glasses" by Gilles Tran (2006)


"Christmas Baubles" by Jaime Vives Piqueres (2005)


"Office" by Jaime Vives Piqueres (2004)

2


"Villarceau Circles" by Tor Olav

Kristensen (2004)


"Autobahn WIP" by Jaime Vives Piqueres (2005)


"Car Study" by René Bui (2006)


Jaime Vives Piqueres (2003)

COSC4328/5327 Computer Graphics 11 COSC4328/5327 Computer Graphics 12

"Small World" by Stephen M. Farrell (2002)

3


"Urban Tree" by Jaime Vives Piqueres (1999)


"Rocket" by Jochen Diehl (2004)


"The Dark Side of the Trees" by

Gilles Tran (2002)

Gilles Tran (2000)


"Techno Garb"

by Samuel Benge

(2003)


"Dancing Cube" by Friedrich A. Lohmueller (2003)


"Balanza" by Jaime Vives Piqueres (2002)

4


"BL Object 5" by Douglas Eichenberg (2003)


"Travieso" by Jaime Vives Piqueres (1997)


"Harvest Time" by Gilles

Tran (1999)

This image won the

IRTC competition of

November - December

1999, "Gardens" topic


"Still with Bolts" by Jaime Vives Piqueres (2002)


© 1994 by Martin Moeck, Siemens Lighting

Radiance Movies COSC4328/5327 Computer Graphics 24

5

Consider This Room.

• When I’m looking towards the wall,

what can I see behind me?

• Do I get any clues about what is

behind me?

• How do we see?

– Our eyes are sensors. What do they

sense?

– We are detecting light at different

wavelengths (roughly)

– Where does this light come from?

– From the desk, the wall, the table?

– From some light source.


Pinhole Camera

• Why a camera?

• Lets use a pinhole camera model.

• Why?

• Should we flip image?


Light Comes Forward

From its Source(s) Forward Tracing

• Can this be done?

• How would we do it?

– Well, we would have to trace all

rays from all lights.

– If they end up hitting our eye

(camera) then we add in it’s

contribution.

• Is this efficient?

• Is it accurate?

• What could we do instead?

Tracing from light source

Traditional ray-tracing

Yes

No

Yes

Backward Tracing

Basic Ray Casting

Method

• pixels in screen

– Shoot ray 𝑝 from the eye through

the pixel.

– Find closest ray-object intersection.

– Get color at intersection

6

Basic Ray Casting

Method



the pixel.



Basic Ray Casting

Method



the pixel.



Basic Ray Casting

Method



the pixel.



Basic Ray Model

• Let’s treat a ray as a vector. Namely

we can represent a ray by the vector

form:

𝑝 = 𝑢 + 𝑣 𝑡

Basic Ray Model



form:

𝑝 = 𝑢 + 𝑣 𝑡

• where:

𝑝 is any point along the ray

Basic Ray Model



form:

𝑝 = 𝑢 + 𝑣 𝑡

• where:


𝑢 is the starting point

7

Basic Ray Model



form:

𝑝 = 𝑢 + 𝑣 𝑡

• where:



𝑣 is the direction

Basic Ray Model



form:

𝑝 = 𝑢 + 𝑣 𝑡

• where:



𝑣 is the direction

𝑡 is how far we’ve travelled along ray.

Ray/Sphere Intersection

• Let’s use a sphere of radius 1 centered

at the origin

• In vector form

• The ray 𝑝 intersects the sphere when

𝑝 = 𝑢 + 𝑣 𝑡 satisfies the equation for

the sphere.

• Plug in the ray into sphere equation

• Let’s expand

• We have a lot of vector times vector

operations? What is that? What is the

result?

𝑥2 + 𝑦2 + 𝑧2 = 1

𝑝 2 = 1

𝑝 2 = 1 𝑝 = 𝑢 + 𝑣 𝑡

𝑢 + 𝑣 𝑡 2 = 1

𝑢2 + 2𝑢𝑣 𝑡 + 𝑣 2𝑡2 = 1


• Solve using quadratic formula

• Let’s solve this in three steps.

1. if 𝑏2 ≤ 4𝑎𝑐, we don’t get a solution.

if 𝑏2 = 4𝑎𝑐, 𝑝 is a tangent ray, which

we can consider a miss.

2. if 𝑏 > 0 then 𝑡1 = −𝑏− 𝑏2−4𝑎𝑐

2𝑎 else

𝑡1 = −𝑏+ 𝑏2−4𝑎𝑐

2𝑎

3. 𝑡2 =𝑐

𝑎𝑡1

𝑢2 + 2𝑢𝑣 𝑡 + 𝑣 2𝑡2 = 1

𝑐 𝑏 𝑎

𝑢2 − 1 + 2𝑢𝑣 𝑡 + 𝑣 2𝑡2 = 0

rad=b*b-4*a*c

if (rad <= 0) return no int

if (b > 0)

t1 = (-b-sqrt(rad))/(2*a)

else

t1 = (-b+sqrt(rad))/(2*a)

T2 = c/(a*t1);


D = B*B - 4*AC;

if (D < 0.0) return NULL;

rootD = sqrt(D);

t0 = 0.5*(-B - rootD)/A;

t1 = 0.5*(-B + rootD)/A;

if (t0 >= 0)

hit->t = t0, return hit;

if (t1 >= 0)

hit->t = t1, return hit;

return NULL;

* / + -

A 3+1+1 1+1 1 1+2+1 1

B 3+1+1 1+1 1+2 1

rad=b*b-4*a*c

if (rad <= 0) return no int

if (b > 0)

t1 = (-b-sqrt(rad))/(2*a)

else

t1 = (-b+sqrt(rad))/(2*a)

T2 = c/(a*t1);

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