Instructions
- 0-9: Change untuck coefficient.
- c: Move points to control vertices.
- r: Insert a new vertex at the midpoint of each existing vertex
- d: Decimate and compute Laplace
- t: Perform tuck operation
- u: Perform untuck operation
- f: Perform 'tuck-untuck'
- j: Perform Jarek subdivision
- y: Update and compute Laplace
- >: Increase tuck coefficient
- <: Decrease tuck coefficient
- +: Increase untuck coefficient
- -: Decrease untuck coefficient
- p: Toggle highlighting vertices
- P: Toggle showing highlighted Laplace dots
- s: Save points
- S: Save new points
- l: Load points
- a: Axis-align edges
- g: Toggles animation
- x: Selects a sample at every 16th point
- z: Distributes the samples along a refined curve
- q: Makes new curve from these samples
- e: Poor man's uniform resampling
- E: Equidistant uniform resampling (real-space, not parameter space)
- b: Show dot at mouseX/width along the parameterized curve.
Explanation/Source
Naive Resampling vs. Equidistant Resampling
The naive resampling simply takes a refined curve and tells points to move towards their further neighbor by one vertex step. This is processor intensive because it requires that the curve be refined a number of times before it can be processed. However, it is a simple approach and inherently understandable.
Our approach was to create points along the curve that are an equal distance in space (not along a parameterization) from each other. This is done by computing the length of the entire curve and then moving along that curve in real-space increments, placing a new dot where a circle intersects the curve at a later point. The advantages to this method are relative speed as well as having a uniform distance between vertices, giving a smooth animation effect.
Equidistance
In our case, the points are equidistant. We implemented the more difficult (real-space equidistant) version of the resampling algorithm from the beginning, and so doing the parameterized version would simply be walking an equal parameter length that is determined by the total length (which we can compute) and the number of vertices (which we know).