Project 2c © Jorg Peters

Points: 30

Task 1: Cage-based deformation

Points: 10

Place the N points P_i into the four triangles of a quincunx pattern Q_j where Q₀ is the central point of the square, initially at (0,0).

Make all 5 points of Q movable.

Determine the barycentric coordinates of each point with respect to the four triangles and only retain the triple of positive ones (ie the ones with respect to the triangle into which the point falls)

Move the central point Q₀ and update the P_i by placing them at their barycentric coordinates with respect to the modified triangles.

Deform the original subdivision curve by moving Q₀.

Computer graphics demonstration showing a curve and control points in a dark blue window. A square with a cross, the quincunx pattern, encloses all points — Figure 1. Reference image for Cage-based deformation

Task 2: 3D Picking and Dragging

Points: 5

When the Shift key is pressed on the keyboard, horizontal mouse motion moves B-spline control points P_i in the z-direction. This motion is not yet visible.

Computer graphics demonstration showing a curve and control points in a dark blue window. A selected yellow control point is connected to nearby green control points; red marks appear along the curve. — Figure 2. Reference image for 3D picking and dragging.

Task 3: Double View

Points: 10

In the top half of the window, draw the default view perpendicular to the x-y plane.
In the bottom half of the window, draw the side view perpendicular to the y-z plane.
Toggle the double view when the 4 key is pressed.
Picking needs to work only in Single View.

Two-view computer graphics display on a dark blue background. The upper view shows a figure-eight-like curve with control points; the lower view shows a side projection of the same curve and its control polygon. — Figure 3. Reference image for the double-view display.

Task 4

Points: 5

On key 5 press, toggle on or off a suitably large yellow dot traveling around the closed BB-curve. This is an animation.
Draw the tangent in red, the normal in green, and the bi-normal in blue at the yellow dot. Together these vectors form the Frenet frame of the curve.

What to Submit

Readme.txt: explain each task that was implemented and each task that was not implemented.
A ZIP archive of the project folder.
A link to a screen capture of your running program showcasing the implementation of all tasks using Recordit (Mac, Windows), or similar software.