3
votes
1answer
68 views

inflection point of cubic bezier with restrictions

Say you have this type of cubic Bézier curve: The 4 control points A,B,C,D have restrictions: A & B have the same Y-axis coordinate C & D have the same Y-axis coordinate B & C have ...
1
vote
1answer
23 views

Prove monotocity of cubic Bezier's curve under certain restrictions

Suppose I have a cubic bezier curve with the points $(x_0, y_0); (x_1, y_1); (x_2, y_2); (x_3, y_3)$. I want to show that the resulting function is monotonic for $x$ for the following restrictions: ...
1
vote
1answer
33 views

How to take derivative of Bezier function?

I am trying to figure out how to take the derivative of the following quadratic Bezier equation, with respect to 't' for the set of numbers between $0$ and $1$. I understand how to take the derivative ...
1
vote
1answer
136 views

Gradient of a rational Bezier curve

I'd appreciate help working out the gradient of a rational Bezier curve $C = (\,x(t) \,, \,C_y(t) \,)$. I know that the gradient $g$ of a the parametric curve is $$ g(t) = \left( \frac{dy(t)}{dt} ...
1
vote
1answer
396 views

Finding point of inflection on a Bézier Curve

I need to determine the first point of inflection on a Bézier curve, if it exists, for a computer graphics application. My original idea was to iteratively walk the curve, evaluating 2nd derivatives ...
0
votes
0answers
623 views

Subdividing a cubic Bezier curve at an arbitrary point

I want to subdivide a cubic Bezier curve at a point which may not be the curve's midpoint. I'm using the plain and slow incremental method to plot the curve from its parametric equations.
2
votes
1answer
805 views

Equation for control point distance for fixed-length cubic Bézier path (with specific constraints)

A particular Stack Overflow question asks how to construct a specific cubic Bézier path of constant length. I have experimentally determined the ideal distances of the control points from the nearest ...
1
vote
1answer
235 views

Bézier Curve and Gravitational Pull

Okay, so I'm trying to manipulate an object programmatically. When it gets near another object, lets say a globe. I want the globe to have a gravitational pull on the original object. This isn't so ...
1
vote
1answer
579 views

Finding the parameter of a quadratic Bézier curve for which the tangent passes through a point

I am currently working on a program that requires me to deal with quadratic Bézier curves (basically, I have to take a curve and draw it with a specified thickness). In order to do so, I create two ...
1
vote
1answer
296 views

Parabola attributes - custom curve?

UPDATE: I feel like my original question was too vague and didn't provide enough information (as others have mentioned). So I'm going to restate it. Purpose: I want to find an equation in order to ...