Rotation Fix Attempt 1 - Demo 08

Purpose

Fix the rotation problem from the previous demo in a seemingly intuitive way, but do it inelegantly.

Demo 08

Demo 08

How to Execute

On Linux or on MacOS, in a shell, type “python src/demo08/demo.py”. On Windows, in a command prompt, type “python src\demo08\demo.py”.

Move the Paddles using the Keyboard

Keyboard Input

Action

w

Move Left Paddle Up

s

Move Left Paddle Down

k

Move Right Paddle Down

i

Move Right Paddle Up

d

Increase Left Paddle’s Rotation

a

Decrease Left Paddle’s Rotation

l

Increase Right Paddle’s Rotation

j

Decrease Right Paddle’s Rotation

Description

The problem in the last demo is that all rotations happen relative to World Space’s (0,0) and axes. By translating our paddles to their position before rotating, they are rotated around World Space’s origin, instead of being rotated around their modelspace’s center.

In this demo, we try to solve the problem by making a method to rotate around a given point in world space, in this case, the paddle’s center.

src/demo08/demo.py
109class Vertex:
src/demo08/demo.py
143    def rotate_around(self: Vertex, angle_in_radians: float, center: Vertex) -> Vertex:
144        translate_to_center: Vertex = self.translate(-center)
145        rotated_around_origin: Vertex = translate_to_center.rotate(angle_in_radians)
146        back_to_position: Vertex = rotated_around_origin.translate(center)
147        return back_to_position

Within the event loop, this seems quite reasonable

src/demo08/demo.py
218while not glfw.window_should_close(window):
src/demo08/demo.py
237    glColor3f(paddle1.r, paddle1.g, paddle1.b)
238
239    glBegin(GL_QUADS)
240    rotatePoint: Vertex = paddle1.position
241    for paddle1_vertex_in_model_space in paddle1.vertices:
242        paddle1_vertex_in_world_space: Vertex = paddle1_vertex_in_model_space.translate(paddle1.position)
243        paddle1_vertex_in_world_space: Vertex = paddle1_vertex_in_world_space.rotate_around(paddle1.rotation,
244                                                        rotatePoint)
245        paddle1_vertex_in_ndc_space: Vertex = paddle1_vertex_in_world_space.uniform_scale(scalar=1.0/10.0)
246        glVertex2f(paddle1_vertex_in_ndc_space.x, paddle1_vertex_in_ndc_space.y)
src/demo08/demo.py
253    # draw paddle 2
254    glColor3f(paddle2.r, paddle2.g, paddle2.b)
255
256    glBegin(GL_QUADS)
257    rotatePoint: Vertex = paddle2.position
258    for paddle2_vertex_model_space in paddle2.vertices:
259        paddle2_vertex_world_space: Vertex = paddle2_vertex_model_space.translate(paddle2.position)
260        paddle2_vertex_world_space: Vertex = paddle2_vertex_world_space.rotate_around(paddle2.rotation,
261                                                        rotatePoint)
262        paddle2_vertex_ndc_space: Vertex = paddle2_vertex_world_space.uniform_scale(scalar=1.0/10.0)
263        glVertex2f(paddle2_vertex_ndc_space.x, paddle2_vertex_ndc_space.y)
264    glEnd()

All we did was add a rotate around method, and call it, with the paddle’s center as the rotate point.

Works but sloppy

Although this works for now and looks like decent code, this is extremely sloppy, and not thought out well at all. We apply a transformation from paddle space to world space, then do the inverse, then rotate, and then do the first transformation from paddle space to world space again.

The images of the transformation sequence below should show how brain-dead it is, and the Cayley graph is gross.

But from this we will learn something important.

Demo 08

translating back to the origin

Demo 08

resetting the coordinate system

Demo 08

rotating

Demo 08

resetting the coordinate system

Demo 08

and them translating them back to the paddle space origin

Demo 08

Cayley Graph

Note, this is gross, and the edge from the paddlespace to itself doesn’t even make any sense, but the author did not know how else to represent this code.

Demo 08