1. Applying Geometric Transformations
CSE 3541/5541
Matt Boggus

2. Outline Operations and the benefit to using them
Translate
Rotate
Scale
Relevant Unity scripting features

3. Common 2D transformations
In class visualization of translate, rotate, scale

4. Translating an object
Translate individual
vertices by the same vector

5. Rotating an object q
Rotate individual
vertices by the same angle

6. Scaling an object Scale individual vertices by the same vector (4,4)
(2,2)
(4,4)
(1,1)
(2,2)
Sx = 2, Sy = 2
Scale individual
vertices by the same vector

7. Animation by re-use of model and applying transformations over time
Fortress Quest
Compare cost or effort to create main character motion to that from hand-drawn example shown in the animation history slides

8. Vectors (and Points) in Unity
Vector2 (reference page)
Vector3 (reference page)
Vector4 (reference page)

9. Vector3 Data members Operations/Operators x,y,z floats set(x,y,z)
+,- vector-vector operations
*,/ vector-scalar operations
== comparison (has some flexibility to handle nearly equal values)
Normalize, Distance, Dot

10. Code example with Vector3
In a script attached to a GameObject: Vector3 temp; temp = new Vector3(3,5,8); transform.position = temp;

11. Transformations in Unity
transform (reference)
Position, rotation, and scale of an object
Methods
Translate
Rotate
Data
position
rotation

12. transform.Translate function Translate ( translation : Vector3,
relativeTo : Space = Space.Self )
translation vector – tx,ty,tz
Space.Self – local coordinate system
Space.World – world coordinate system

13. transform.Rotate function Rotate ( eulerAngles : Vector3,
relativeTo : Space = Space.Self )
Applies a rotation
eulerAngles.z degrees around the z axis, eulerAngles.x degrees around the x axis, and
eulerAngles.y degrees around the y axis
(in that order).

14. transform.Rotate function Rotate ( eulerAngles : Vector3,
relativeTo : Space = Space.Self )
Space.Self – rotate about local coordinate frame (center of prebuilt GameObjects, could be anywhere for an artist made model)
Space.World – rotate about world coordinate frame (origin (0,0,0))

15. On your own activity with transform.Rotate
In your script for lab1, in Update() add the statement
transform.Rotate(0,1,0);
Run the animation and hold down the ‘a’ key, is the result what you were expecting?
Try it again with
transform.Rotate(0,1,0, Space.World);
Also experiment with using Space.World in a call to Translate