Lecture 7: Intro to Geometry, Splines, and Bezier Curves (61)
waleedlatif1
In the example listed here, we only ever take the distance between points with maximum one point between them, but I was wondering if it would reveal any extra information (potentially useful?) to us if we calculated the tangent line from say y0 to y1, and y2 to y1 or whether that would be extra information that would complicate our calculations.
Staffethanweber
Interesting question! I guess you could do that, though I guess the main benefit of Catmull-Rom is being able to apply this procedure iteratively by sliding along the points, where we can guarantee that we have C1 continuity every and the curve interpolates the points (meaning it goes through them). Maybe there are ways to leverage other point combinations for more properties.
In the example listed here, we only ever take the distance between points with maximum one point between them, but I was wondering if it would reveal any extra information (potentially useful?) to us if we calculated the tangent line from say y0 to y1, and y2 to y1 or whether that would be extra information that would complicate our calculations.
Interesting question! I guess you could do that, though I guess the main benefit of Catmull-Rom is being able to apply this procedure iteratively by sliding along the points, where we can guarantee that we have C1 continuity every and the curve interpolates the points (meaning it goes through them). Maybe there are ways to leverage other point combinations for more properties.