Modify the program in Exercise 29 to have the square...

Name: Problem 31, Chapter 5: Computer Graphics with Open GL
Uploaded: 2021-04-25T18:41:20-08:00
Duration: 2 min 51 s
Channel: Aaron Goree
Description: Modify the program in Exercise 29 to have the square additionally "pulse" as it moves along its path. That is, for every revolution about its own center that it makes, it should go through one pulse cycle that begins with the square at full size, reduces smoothly in size down to 50 normal size by the end of the cycle. Do this using only basic OpenGL geometric transformations.

Modify the program in Exercise 29 to have the square additionally "pulse" as it moves along its path. That is, for every revolution about its own center that it makes, it should go through one pulse cycle that begins with the square at full size, reduces smoothly in size down to 50 normal size by the end of the cycle. Do this using only basic OpenGL geometric transformations.

Key Concepts

OpenGL Geometric Transformations

OpenGL provides a suite of basic geometric transformations such as translation, rotation, and scaling, which are applied to objects through transformation matrices. These functions allow developers to manipulate objects' positions, orientations, and sizes within the rendered scene. Understanding these transformations is essential to modify shapes dynamically, as they enable complex effects like moving, rotating, and pulsing animations without altering the object's original geometry.

Transformation Order and Hierarchical Modeling

The order in which transformations are applied is critical in achieving desired visual effects because subsequent transformations are compounded on those applied previously. In hierarchical modeling, transformations can be grouped to create complex motions where one transformation, such as a rotation around a center, can be combined with another transformation, like a scaling effect to simulate pulsing. Mastery of transformation ordering allows precise control over the animation of composite movements.

Animation Timing and Synchronization

Animation timing involves controlling when and how transformations occur over a period. Synchronizing the scaling (pulse) cycle with the object's rotation or revolution cycle requires the use of timing parameters. By calculating proportions of the rotation or elapsed time, developers can ensure that the pulse effect—gradually reducing the size to a fraction and then returning to normal—occurs in a smooth and predictable manner for every revolution.

Transcript

00:01 This problem is asking us to prompt the user for some input about the center of the circle.

00:07 And then we're going to do some math to find the area of the circle.

00:12 And finally, we're going to draw it.

00:15 So let's look at one method to do that.

00:18 Take a look up here.

00:20 I'm talking about using the center coordinates to find the bottom of the circle.

00:24 We need to find the bottom of the circle to start drawing it.

00:27 So we'll do that later.

00:29 But first, let's import our turtle.

00:33 To say turtle dot done down here at the bottom so we don't forget we prompt our user for some input values i want to prompt the user to input the center coordinates and the radius of the circle now that we've got those coordinates and the radius we can do some math computer area we're going to do that by creating a constant named pi and then creating a variable called area where we can use the formula pi times the radius squared, just like that.

01:20 So now we have our area.

01:22 We're ready to draw our circle.

01:25 The turtle always draws starting at the bottom.

01:33 So right here, if we were to go to this coordinate, that would take us to the center of the circle.

01:38 I want to start drawing at the bottom of the circle, so i'm going to take our y coordinates and go below the center by saying minus radius.

01:51 Now we're ready to draw...

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