Se 313 computer graphics
Download
1 / 28

SE 313 – Computer Graphics - PowerPoint PPT Presentation


  • 75 Views
  • Uploaded on

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

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

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

SE 313 – Computer Graphics

Lecture 8: Transformations and Projections

Lecturer: GazihanAlankuş


Plan for today
Plan for Today

  • Post-exam talk

  • Revisit transformations

  • Projections


Exam talk
Exam Talk

  • Go over exam questions


Transformations summary
Transformations (summary)

  • Three types of linear transformations

    • Translation (point-vector addition)

    • Rotation (3x3 matrix multiplication)

    • Scale (vector-scalar multiplication)


Transformations summary1
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 summary2
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 summary3
Transformations (summary)

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

Rotation and scale

Translation

0

0

0

1


Transformations summary4
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 summary5
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 summary6
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 today1
Plan for Today

  • Post-exam talk

  • Revisit transformations

  • Projections


Projection
Projection

  • Projections from 3D to 2D

    • Taking pictures of the virtual world

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


Projection types
Projection Types

  • Perspective projection

    • Just like our eyes and cameras

  • Orthographic projection

    • Architectural drawing with no distance distortion


Orthographic vs perspective projection
Orthographic vs. Perspective Projection

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


Orthographic projection
Orthographic Projection

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

[engineeringtraining.tpub.com]


Orthographic projection1
Orthographic Projection

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

  • No depth sensation


Orthographic projection in blender
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
Perspective Projection

  • Take the picture of the world from a single point


Perspective projection1
Perspective Projection

  • What parameters do I need?



Perspective projection3
Perspective Projection

  • How do you do it mathematically?

    • Also using a 4x4 matrix

[songho.ca]


Perspective projection4
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 projection5
Perspective Projection

  • What that matrix does


Perspective projection in blender
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
Perspective vs Orthographic Projection

Fov=60◦, distance = 1

Fov=30◦, distance = 3

Perspective

Fov=10◦, distance = 5

Fov=0◦, distance =

Orthographic


Perspective vs orthographic projection1
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 projection2
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
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


ad