One interesting application of this 2d Bezier interpolation is in Photoshop. One of the effects that you can use on an image is a 3D warp, where photoshop gives you a mesh of 16 control points that you can drag around. Now I realize that photoshop's actually deforming the image in 3D space, using a Bezier surface, and then projecting it back onto the image plane!
john-b-yang
I'm trying to understand why the array's dimensions must be 4x4. I really like the demo on the next slide, but couldn't the same surface patch be achieved with a 5x5 array? Is there any reason it's 4x4, or is that arbitrary?
sheaconlon
@john-b-yang The control points are 4x4 because you are parameterizing a surface which is composed of 4 rows of cubic functions with 4 degrees of freedom each. You need 16 inputs in order to uniquely constrain the surface. This is like how in 1D you need to specify 4 points in order to uniquely constrain a cubic function.
One interesting application of this 2d Bezier interpolation is in Photoshop. One of the effects that you can use on an image is a 3D warp, where photoshop gives you a mesh of 16 control points that you can drag around. Now I realize that photoshop's actually deforming the image in 3D space, using a Bezier surface, and then projecting it back onto the image plane!
I'm trying to understand why the array's dimensions must be 4x4. I really like the demo on the next slide, but couldn't the same surface patch be achieved with a 5x5 array? Is there any reason it's 4x4, or is that arbitrary?
@john-b-yang The control points are 4x4 because you are parameterizing a surface which is composed of 4 rows of cubic functions with 4 degrees of freedom each. You need 16 inputs in order to uniquely constrain the surface. This is like how in 1D you need to specify 4 points in order to uniquely constrain a cubic function.