What does "tangent" mean here? From derivation it seems that the derivative at end point is something like n*(p1 - p0)?
xiaol3
The points p1, p2 seems kind of random here. How do they affect how the curve looks like exactly?
dranzer
As mentioned in the previous slide, I think the control points are important to specify characteristics of our curve. The height of the curve in the various sections and the amount of curvature (i.e tangent). I hope this intuition is correct. They essentially are knobs for you to make say a human's head more rounder, taller or any other shape you would like. In that respect, is there a tool we can play around with to see the effects of different control points ?
keenan
@zhenliz Usually when you say two shapes are tangent you just mean their tangents are parallel. It's not a statement about magnitude.
keenan
@xiaol3 The points p0 and p3 directly control the endpoints; the points p1 and p2 effectively control the direction of the tangents at endpoints (and the magnitude, up to a constant factor).
keenan
@dranzer Sure---open up any drawing tool, like Illustrator or Inkscape, and the pen tool lets you directly manipulate the control points for a Bezier curve. Usually, clicking lets you specify the endpoints; dragging after clicking is giving you control over the tangents. There seem to be a lot of online tools of this type, e.g., https://editor.method.ac/
What does "tangent" mean here? From derivation it seems that the derivative at end point is something like n*(p1 - p0)?
The points p1, p2 seems kind of random here. How do they affect how the curve looks like exactly?
As mentioned in the previous slide, I think the control points are important to specify characteristics of our curve. The height of the curve in the various sections and the amount of curvature (i.e tangent). I hope this intuition is correct. They essentially are knobs for you to make say a human's head more rounder, taller or any other shape you would like. In that respect, is there a tool we can play around with to see the effects of different control points ?
@zhenliz Usually when you say two shapes are tangent you just mean their tangents are parallel. It's not a statement about magnitude.
@xiaol3 The points p0 and p3 directly control the endpoints; the points p1 and p2 effectively control the direction of the tangents at endpoints (and the magnitude, up to a constant factor).
@dranzer Sure---open up any drawing tool, like Illustrator or Inkscape, and the pen tool lets you directly manipulate the control points for a Bezier curve. Usually, clicking lets you specify the endpoints; dragging after clicking is giving you control over the tangents. There seem to be a lot of online tools of this type, e.g., https://editor.method.ac/