Splines in Computer Graphics

Fall 1997

Student: Anna Kagan
Instructor: Dr. Valerie A. Miller

• Single spline segment
• Multi-segment splines
• 4x4 Bezier 3D sample
• 10x10 Bezier 3D
• Experimenting with colors: 4x4 3D sample
• 2D & 3D coloring
• Cylinder

Single spline segment

APPLET

Please note the following:

• First, add 4 points by clicking on the empty plane. When adding points, please don't put them VERY close to each other or on the top of each other. I didn't have a chance to handle such cases.
  
• After ALL FOUR POINTS are displayed, you should see the graph. You can change the graph by dragging the control points. Once again, please don't put the control points on the top of each other: they will merge into one point. I will continue working on this.
  
• Also, don't move or put the points outside the applet plane - you will "loose" them.
  
• The spline you will see (hopefully) is NOT a Bezier spline. I used the formulas 3.23, 3.24 (Numerical Analysis pg.151). The purpose was to compare the graphs with those on pg.152.
  

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Multi-segment splines

BEZIER SPLINE - may (but doesn't have to) be extended to 4 segments

B-SPLINE - may (but doesn't have to) be extended to 20 points

I fixed some bugs found in the single-segment applet. Now you can set points very close to each other and even on the top of each other. When one point is on the top of another, the attempt to move this "two-in-one" point will result in moving the "oldest" point, based on the sequence in which the points were added to the applet.

Additional features:

• You can move ANY point at any time, i.e. it is not necessary to have ALL points to have the graph.
• The points can be added by a SINGLE click. The points will NOT be added if you press the mouse button, drag the mouse, and then release the button. This is done purposely so that adding the point won't be confused with any other actions; therefore, do NOT move the mouse when adding points.
• Try NOT to drag the points TOO FAST. A fast drag won't break anything, but it will make it harder to see the graph change.
• Again, do NOT drag the points beyond the applet plane.

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4x4 Bezier 3D sample

APPLET

Please move only INTERIOR points.
Do NOT move any points on the grid border.

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10x10 Bezier 3D

APPLET

I did not implement 3D B-spline: there are no points that 'belong' to the grid, so moving any of the points brings everything out of control.

Again, please don't move points which are on the grid's border.

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Experimenting with colors: 4x4 3D sample

APPLET

The color is now changing depending on the distance from the grid plane. The original grid is blue; the color becomes lighter when moving farther from the grid.

The smoothness of color change depends on your video adapter.

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2D & 3D coloring

AREA SAMPLE
In this applet you can only move two control points. Only the area ABOVE the axis AND underneath the curve is colored.

SURFACE SAMPLE
There is ONLY ONE point you can move - the one which is already above the surface when the applet starts.

POLYGON MESH SAMPLE
This is, what I, probably, had to start from. The only problem is that the polygons are NOT flat. Again, there is just one point for you to move.

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Cylinder

NON-COLORED

COLORED

Notice that all non-visible parts of the frame are white, while visible parts are blue.

Although you can move control points (red) in both applets, I do NOT recommend to do this in COLORED applet since it takes quite long time to recolor.

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Last update: Nov.4, 1998
anna_mcp@msn.com