1 / 28

SE 313 – Computer Graphics - PowerPoint PPT Presentation

SE 313 – Computer Graphics. Lecture 8 : Transformations and Projections Lecturer: Gazihan Alankuş. Plan for Today. Post-exam talk Revisit transformations Projections. Exam Talk. Go over exam questions. Transformations (summary). Three types of linear transformations

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about ' SE 313 – Computer Graphics' - quanda

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

SE 313 – Computer Graphics

Lecture 8: Transformations and Projections

Lecturer: GazihanAlankuş

• Post-exam talk

• Revisit transformations

• Projections

• Go over exam questions

• Three types of linear transformations

• Translation (point-vector addition)

• Rotation (3x3 matrix multiplication)

• Scale (vector-scalar multiplication)

• Three types of linear transformations

• Translation (point-vector addition)

• Rotation (3x3 matrix multiplication)

• Scale (vector-scalar multiplication)

• Cannot combine these operations in one type of operation

• Convert them to one type of operation (not possible unless you use homogeneous coordinates)

• Homogeneous coordinates enable us to represent translation, rotation and scale using 4x4 matrix multiplications.

• This way we can combine them easily by multiplying matrices together. The resulting matrix is another transformation.

• 4x4 matrices that are combinations of translation, rotation and scale

Rotation and scale

Translation

0

0

0

1

• You can read the local coordinate frame from 4x4 transformation matrices

Rotation and scale

Translation

The x, y and z axes of thelocal frame

Where in the world the local frame’s origin is

0

0

0

1

• Intuitive understanding of transformations

• Local-to-world: insert new transformations near the wall (world)

• World-to-local: insert new transformations near the object

• Quaternions: data structure for rotation

• Useful for animations

• Ways of representing rotations

One axis, one angle

3x3 matrix

Quaternion

Three angles (euler angles)

Best interpolation (slerp)

Great-looking animations

• Post-exam talk

• Revisit transformations

• Projections

• Projections from 3D to 2D

• Taking pictures of the virtual world

[Images are borrowed from http://db-in.com]

• Perspective projection

• Just like our eyes and cameras

• Orthographic projection

• Architectural drawing with no distance distortion

[Images are borrowed from http://db-in.com]

• Get the 3D world, compress it on a 2D paper

[engineeringtraining.tpub.com]

• Great for isometric games (Starcraft, Diablo I-II)

• No depth sensation

• Select the camera

• The viewport is defined by the render output size

• Camera has

• Scale

• Start and end clipping distances

• Take the picture of the world from a single point

• What parameters do I need?

• How do you do it mathematically?

• Also using a 4x4 matrix

[songho.ca]

• Let’s try to make sense of it very simply

0

0

0

0

0

0

Translating in z

0

0

-1

0

Output’s w depends on input’s z

The further it is in z, the smaller it will get

• What that matrix does

• Select the camera

• The viewport is defined by the render output size

• Camera has

• Field of view angle

• Start and end clipping distances

Fov=60◦, distance = 1

Fov=30◦, distance = 3

Perspective

Fov=10◦, distance = 5

Fov=0◦, distance =

Orthographic

• Orthographic camera is a perspective camera where the camera is at the infinity and the field of view angle is zero

• In this transition, the size of the arrow in the image stays the same

• This is also "called the “dolly-zoom”,“Hitchcock zoom”, or “vertigo effect”

• Demonstration in Unity and sample scenes from movies

• No homework

• Study what we learned today, there will be a quiz

• Next week, a part of the lab will be about projection