raytracing render with trianglessking/courses/cosc5327/notes/raytracing-6.pdf1 raytracing cosc...

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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)

COSC4328/5327 Computer Graphics 4

"Glasses" by Gilles Tran (2006)

COSC4328/5327 Computer Graphics 5

"Christmas Baubles" by Jaime Vives Piqueres (2005)

COSC4328/5327 Computer Graphics 6

"Office" by Jaime Vives Piqueres (2004)

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COSC4328/5327 Computer Graphics 7

"Villarceau Circles" by Tor Olav

Kristensen (2004)

COSC4328/5327 Computer Graphics 8

"Autobahn WIP" by Jaime Vives Piqueres (2005)

COSC4328/5327 Computer Graphics 9

"Car Study" by René Bui (2006)

COSC4328/5327 Computer Graphics 10

Jaime Vives Piqueres (2003)

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

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

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COSC4328/5327 Computer Graphics 13

"Urban Tree" by Jaime Vives Piqueres (1999)

COSC4328/5327 Computer Graphics 14

"Rocket" by Jochen Diehl (2004)

COSC4328/5327 Computer Graphics 15

"The Dark Side of the Trees" by

Gilles Tran (2002)

Gilles Tran (2000)

COSC4328/5327 Computer Graphics 16

"Techno Garb"

by Samuel Benge

(2003)

COSC4328/5327 Computer Graphics 17

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

COSC4328/5327 Computer Graphics 18

"Balanza" by Jaime Vives Piqueres (2002)

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COSC4328/5327 Computer Graphics 19

"BL Object 5" by Douglas Eichenberg (2003)

COSC4328/5327 Computer Graphics 20

"Travieso" by Jaime Vives Piqueres (1997)

COSC4328/5327 Computer Graphics 21

"Harvest Time" by Gilles

Tran (1999)

This image won the

IRTC competition of

November - December

1999, "Gardens" topic

COSC4328/5327 Computer Graphics 22

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

COSC4328/5327 Computer Graphics 23

© 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.

COSC4328/5327 Computer Graphics 25

Pinhole Camera

• Why a camera?

• Lets use a pinhole camera model.

• Why?

• Should we flip image?

COSC4328/5327 Computer Graphics 26

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

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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

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

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

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

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

we can represent a ray by the vector

form:

𝑝 = 𝑢 + 𝑣 𝑡

• where:

𝑝 is any point along the ray

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

• where:

𝑝 is any point along the ray

𝑢 is the starting point

7

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

• where:

𝑝 is any point along the ray

𝑢 is the starting point

𝑣 is the direction

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

• where:

𝑝 is any point along the ray

𝑢 is the starting point

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

Ray/Sphere Intersection

• 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);

Ray/Sphere Intersection

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);