9-Transformations

# 9-Transformations - Modeling Transformations Jason Lawrence...

This preview shows pages 1–18. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Modeling Transformations Jason Lawrence CS 4810: Graphics Acknowledgment: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David Dobkin Overview • 2D Transformations Basic 2D transformations Matrix representation Matrix composition • 3D Transformations Basic 3D transformations Same as 2D Simple 2D Transformations Translation x y P P’ Simple 2D Transformations Translation x y Simple 2D Transformations Scale x z y Simple 2D Transformation Rotation x z y 2D Modeling Transformations Scale Rotate Translate Scale Translate x y World Coordinates Modeling Coordinates 2D Modeling Transformations x y World Coordinates Modeling Coordinates Let ʼ s look at this in detail… 2D Modeling Transformations x y Modeling Coordinates 2D Modeling Transformations x y Modeling Coordinates Scale .3, .3 Rotate -90 Translate 5, 3 2D Modeling Transformations x y Modeling Coordinates Scale .3, .3 Rotate -90 Translate 5, 3 2D Modeling Transformations x y Modeling Coordinates Scale .3, .3 Rotate -90 Translate 3, 5 World Coordinates Basic 2D Transformations • Translation: x ʼ = x + tx y ʼ = y + ty • Scale: x ʼ = x * sx y ʼ = y * sy • Rotation: x ʼ = x*cos Θ- y*sin Θ y ʼ = x*sin Θ + y*cos Θ Transformations can be combined (with simple algebra) Basic 2D Transformations • Translation: x ʼ = x + tx y ʼ = y + ty • Scale: x ʼ = x * sx y ʼ = y * sy • Rotation: x ʼ = x*cos Θ- y*sin Θ y ʼ = x*sin Θ + y*cos Θ Basic 2D Transformations • Translation: x ʼ = x + tx y ʼ = y + ty • Scale: x ʼ = x * sx y ʼ = y * sy • Rotation: x ʼ = x*cos Θ- y*sin Θ y ʼ = x*sin Θ + y*cos Θ x ʼ = x *sx y ʼ = y *sy (x,y) (x ʼ ,y ʼ ) Basic 2D Transformations • Translation: x ʼ = x + tx y ʼ = y + ty • Scale: x ʼ = x * sx y ʼ = y * sy • Rotation: x ʼ = x *cos Θ- y *sin Θ y ʼ = x *sin Θ + y *cos Θ (x ʼ ,y ʼ ) x ʼ = (x*sx) *cos Θ − (y*sy) *sin Θ y ʼ = (x*sx) *sin Θ + (y*sy) *cos Θ Basic 2D Transformations • Translation: x ʼ = x + tx y ʼ = y + ty • Scale: x ʼ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 50

9-Transformations - Modeling Transformations Jason Lawrence...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online