Page 27: Last Page (rubric)

Spring 2026 Sample Solution

You have made it to the end of the third workbook!

This workbook has introduced you to curves. Curves are important for making shapes. While we focused on 2D curves, all the concepts extend to 3D and will provide the basis for how we create surfaces in 3D.

NotebookLM's Summary

I fed the Workbook to Notebook LM to see what an AI had to say about it…

This workbook serves as a comprehensive guide to 2D curves within the context of computer graphics, with a primary focus on parametric representations. It introduces three main mathematical approaches—implicit, parametric, and subdivision—while highlighting why parametric forms like Bézier curves are the industry standard for drawing and design. Students learn critical concepts such as continuity (C and G levels), derivatives for computing tangents and normals, and the geometric construction of curves via the de Casteljau algorithm. The material transitions from simple line segments to complex piecewise polynomials, specifically exploring Hermite, Cardinal, and B-Splines. Practical application is emphasized through technical exercises in Canvas and SVG APIs, culminating in a project to build a functional train track. Key advanced topics like arc-length reparameterization are included to ensure smooth, constant-speed animation and accurate placement of track elements.

Hopefully, you got here by going through every page and completing the work on it. The boxes are the most significant components. Here is a list of all the boxes and whether or not you checked the checkbox. This way you can keep track of what you’ve completed. We will not look at these checks: they are for student convenience.

List of Boxes
Box The box name links back to the box. Check These checkboxes indicate whether you have checked the checkbox for the box. If you didn't check the box, go back to it, make sure the work is completed, and check it. Tag (internal) This is our "internal code name" for the box. Kind Kinds of boxes:
view - look at the box and experiment with it
examine - look at the code for the box
edit - change the box's content
rubric - several steps are suggested in the rubric page - form elements on page in rubric
03-02-01 eg-curves view
03-06-01 ex-curves rubric
03-07-01 eg-two-circles view
03-07-02 eg-draw-two-circles view
03-14-01 eg-bezier view
03-15-01 eg-decasteljau-higher view
03-15-02 eg-decasteljau view
03-17-01 ex-bezier-svg rubric
03-17-02 ex-bezier rubric
03-19-01 eg-arc-length-box view
03-19-02 eg-arc-length-line view
03-19-03 ex-arc-length-triangle rubric
03-19-04 eg-arc-length-curve view
03-20-01 ex-spiral rubric
03-21-01 ex-cardinal rubric
03-21-02 ex-split rubric
03-22-01 ex-canvas-ui rubric
03-22-02 ex-points-ui rubric
03-24-01 ex-train rubric
03-26-01 student rubric

Here is a list of all the box rubric items in this workbook. You should make sure that you have completed all the items you intend to do. They are marked as completed if you have selected the checkbox. You should only check the boxes that you have completed.

Workbook Rubric
Box The box name links back to the box. These checkboxes indicate whether you have checked the box for the rubric item. If you didn't check the box, go back to it, make sure the work is completed, and then check the checkbox. Kind Kind of rubric items:
standard - expected from all students
advanced - used to get a better grade
creative - an opportunity to do something creative
levels - rubric item graded by selected achievement level
optional - not required, but encouraged
Description
03-06-01 X standard implement the correct tangent vector for the parabola
03-17-01 X standard recreated the picture using Canvas
03-17-01 X standard didn't use quadratic commands but got the correct shape using cubics
03-17-02 X standard draw a picture that demonstrates the use of bezierCurveTo in Canvas
03-17-02 X standard explained where there is G(1) continuity between Bézier segments in box
03-19-03 X standard make the green dot go around the triangle with arc-length parameterization
03-20-01 X standard draw the spiral
03-20-01 X standard checkbox and slider controls
03-20-01 X optional approximate spiral with Beziers, have a switch for lines/Beziers
03-21-01 X standard make a cardinal spline through the points
03-21-01 X advanced draw 20 distinct points on the curve
03-21-01 X optional the 20 points have equal arc-length between consecutive points
03-21-02 X standard split the Bezier
03-22-01 X standard canvas UI demo (something spins)
03-22-02 X standard initial hexagon - ui works
03-24-01 X standard Cardinal Spline Track (w/UI)
03-24-01 X standard Train goes around the track (run button)
03-24-01 X standard Train points in the right direction
03-24-01 X standard Initial track shows arc-length problem
03-24-01 X advanced Arc-length parameterization
03-24-01 X advanced Rail Ties
03-24-01 X advanced Parallel Rails
03-24-01 X advanced Multiple Cars
03-24-01 X advanced B-Splines
03-24-01 X creative Trucked Wheels
03-24-01 X creative Smoke
03-24-01 X creative Nicer-Looking Train
03-24-01 X creative Adaptive Scenery
03-26-01 X standard Some curved shapes
03-26-01 X advanced Some curved motion
03-26-01 X creative Something cool

Handing things in…

Please check one more time that your NetID is correct:

Please tell us how you used AI tools in doing this workbook. Remember, disclosing AI usage is part of the class policy on AI usage.

In the following section, you should give attributions for any included work—for example, if you took an image or model from the web.

Check that the local store is correctly written (and the json file has moved to the correct location) - it probably changed after you filled in the AI Note and Attributions.

If you’ve done that, you are ready to submit your workbook!

Make sure to commit and push your work. Then press the “Submit” button to tell us that your assignment is ready for grading.

Google Sheets Submission:waiting for check
You are viewing the solution version of this page. Submission is disabled.

After pressing the Submit button, the File Status may say “The json file does not match the local store” because the submission time is now in the local store. You don’t have to worry about that.

If you’ve made something you are particularly proud of, we encourage you to submit it for the gallery.

Congratulations! You’ve completed Workbook 3.

Link for grading information: rubric.csv