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SE 313 – Computer GraphicsPowerPoint Presentation

SE 313 – Computer Graphics

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Presentation Transcript

Plan for Today

- Post-exam talk
- Revisit transformations
- Projections

Exam Talk

- Go over exam questions

Transformations (summary)

- Three types of linear transformations
- Translation (point-vector addition)
- Rotation (3x3 matrix multiplication)
- Scale (vector-scalar multiplication)

Transformations (summary)

- 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)

Transformations (summary)

- 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.

Transformations (summary)

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

Rotation and scale

Translation

0

0

0

1

Transformations (summary)

- 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

Transformations (summary)

- Intuitive understanding of transformations
- Local-to-world: insert new transformations near the wall (world)
- World-to-local: insert new transformations near the object

Transformations (summary)

- 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

Plan for Today

- Post-exam talk
- Revisit transformations
- Projections

Projection

- Projections from 3D to 2D
- Taking pictures of the virtual world

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

Projection Types

- Perspective projection
- Just like our eyes and cameras

- Orthographic projection
- Architectural drawing with no distance distortion

Orthographic vs. Perspective Projection

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

Orthographic Projection

- Great for isometric games (Starcraft, Diablo I-II)
- No depth sensation

Orthographic Projection in Blender

- Select the camera
- The viewport is defined by the render output size
- Camera has
- Scale
- Start and end clipping distances

Perspective Projection

- Take the picture of the world from a single point

Perspective Projection

- What parameters do I need?

Perspective Projection

- 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

Perspective Projection

- What that matrix does

Perspective Projection in Blender

- Select the camera
- The viewport is defined by the render output size
- Camera has
- Field of view angle
- Start and end clipping distances

Perspective vs Orthographic Projection

Fov=60◦, distance = 1

Fov=30◦, distance = 3

Perspective

Fov=10◦, distance = 5

Fov=0◦, distance =

Orthographic

Perspective vs Orthographic Projection

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

Perspective vs Orthographic Projection

- 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

For next week

- No homework
- Study what we learned today, there will be a quiz
- Next week, a part of the lab will be about projection

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