Questions on Bézier curves, curves that are frequently used in computer graphics.

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0
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1answer
48 views

Generate easing function from hash table/value pairs

I have a hash-table/value-pair list consisting of, what I call, linear control value paired with curved/eased real values. Something like this: 0 = 0 1 = 0.0010000000000000002 2 = ...
0
votes
1answer
72 views

Improvement over gamma correction for brightening images?

I'd like to brighten one of my own images for printing purposes, using a program I made. When I use the formula: pixelBrightness^0.6 to brighten an image (0.6 being an example, and where ...
4
votes
1answer
80 views

Why does the Bezier Curve work?

Recently I've been looking at Bezier curves and trying to understand how they work. I know that a general Bezier curve is given by the equation $$ \vec{\mathbf{B}}(t) = \sum_{k=0}^n{b_{k,\ ...
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2answers
118 views
1
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1answer
186 views

Find cubic Bézier control points given four points

What I need is to generate an SVG file while having a series of (x,y) ready. P0(x0,y0) P1(x1,y1) P2(x2,y2) P3(x3,y3) P4(x4,y4) P5(x5,y5) ... I need to make a ...
1
vote
1answer
100 views

How to plot a smooth curve function from given points

I have several points, how can I plot a smooth curve that pass through those points? Is there any function that I can create or formula that I can use to get all points in the curve? I have read ...
0
votes
1answer
293 views

Calculating control points of Cubic Bézier curve

I'm trying to draw different arcs with a Cubic Bezier curve and my problem is that after reading different blogs that explain it, I can draw only a 90degree arc using this article. Is it possible if I ...
1
vote
2answers
141 views

maximum of a 5th order bezier curve with restrictions

Say you have a Bézier Curve of the 5th order with restrictions on the Control points: P0 & P1 are on a horizontal line P2 & P3 are on a horizontal line P4 & P5 are on a horizontal line ...
1
vote
3answers
44 views

What's the technical term for “ternary interpolation”?

While researching how to render 2D bezier curves given the control points, I found a simple formula and the resource where I found this marked this iterative process as a ternary interpolation and ...
1
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2answers
172 views

How can I limit the amount of curvature of a bezier curve?

I've been creating bezier curves in a program according to a user clicking where the endpoints ought to be with success. Now, I wonder if there is a way to restrict the shapes of the beziers such that ...
0
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1answer
140 views

Calculating originally arc approximated by cubic bezier curve

I have an cubic bezier curve, which is representing an arc by an approximation. The approximation was calculated with the kappa constant: $$ \\k = \frac43*(\sqrt{2}-1) $$ This means, that the ...
0
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1answer
89 views

Continuity of composite Bezier curves

The composite curve S with pieces where c0 = (−1, 1), c1 = (−1, 0), c2 = (0, 0), and d0 = (0, 0), d1 = (1, 0), d2 = (2, 1). What is the order of continuity of s at (0, 0)?
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2answers
414 views

How to find the N control point of a bezier curve with N+1 points on the curve

I have a the set of points my curve has to pass through, 2 of those are the start and end points. I'm looking for a way to find the control points of my bezier curve (mostly quadratic and cubic) by ...
3
votes
2answers
76 views

Number of Curvature Maxima of a 2D Cubic Bezier curve

I am trying to prove that a standard cubic Bezier curve can only have at most 2 curvature maxima over $t \in [0,1]$. Assuming that no 3 adjacent control points are colinear, the curvature will either ...
2
votes
1answer
237 views

B-spline: compute control points given equations and knots?

Assuming a cubic or higher-order 2-D B-spline: if all piecewise polynomial equations for the final spline (and thus the knot vector as well) are already known, is there a relatively "streamlined" ...
2
votes
4answers
997 views

Changing a bezier curve by dragging a point on the curve itself rather than a control point

I'm developing an iPhone app that allows users to cut out part of an image from its background. In order to do this, they'll connect a bunch of bezier curves together to form the clipping path. Rather ...
0
votes
1answer
51 views

Calculating bezier path when target is moving. (And calculate total travel time)

As a response to another question I asked here (2d spaceship movement + eta) someone suggested to use a bezier curve. This is not answering the question, but it can provide the effect I am looking ...
0
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0answers
93 views

Real roots of a quintic polynomial with constraints

This is a question on the edge of math and programming. I pondered about the best way to state the problem: should I provide context, or get straight to the point of the question? Given various ...
0
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1answer
204 views

How to clip Bézier curves using Casteljau's algorithm?

I am attempting to approximate intersections of Bézier curves using iterative clipping. This common method is described here and here. It basically works like this: Find bounding lines outside one ...
2
votes
2answers
746 views

Offseting a Bezier curve

I searched this site and I read that in general it is not possible to calculate offset of a Bezier curve. But is it possible to calculate the offset in some special cases? Obviously, if the Bezier ...
4
votes
1answer
157 views

Distance from point to parabola (quadratic bezier)

I'm trying to draw quadratic bezier curve (as line). I approximate quadratic bezier curve as parabola ($y=x^2$), according to this document ...
1
vote
1answer
287 views

Detect “Kinks” in Parallel Lines to Bezier Curves [x-post]

I feel like this is just as much a mathematics question as it is a programming question so I figured it couldn't hurt to cross post my question here. Original Post: ...
3
votes
1answer
185 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 ...
0
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1answer
214 views

Intersect Ray (Line) vs Quadratic Bezier Triangle

I'm trying to find the intersection between a line segment and a quadratic bezier triangle for my OpenCL real time raytracer. The main recomendations I've seen are to try subdivision, or tensor ...
-1
votes
3answers
291 views

Finding parametric distance on quadratic curve from given $(x,y)$ point

I want to get the parametric distance (the "$t$" value) at a location on a quadratic Bezier curve, given the "$x$" and "$y$" coordinates of the point. I have start point, end point and control point ...
1
vote
2answers
160 views

How do I find equation of this curve?

I need to find equation of the curve as shown below, for which, I need to find equation for upper part. lower part is half circle. upper part is a constant distance from circle with line passing ...
1
vote
1answer
29 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
50 views

Describing Bézier surfaces

I'm having some trouble with Bézier surfaces and I was hoping someone could help me. Question is rather simple: lets say we have 2 Bézier curves with control points: P00,P10,P20,P30 and second ...
1
vote
2answers
199 views

Deformable circle from a cubic Bezier approximation

I plan to draw approximate circles using a piecewise cubic Bezier representation. The representation should use four Beziers and be defined by four interpolating control points (let us call them ...
2
votes
1answer
220 views

Motion on a parametric surface

Please excuse what will surely turn into a long rambling question, full of incorrect terminology. I'm trying to figure out the mathematics of moving on a parametric surface - that is, for some ...
0
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0answers
50 views

Find curve passing through n points

I'm currently trying to find a method to interpolate a curve and find its control points such as the curve passes through n points that I have computed earlier. What I'm trying to do in fact is find ...
2
votes
1answer
133 views

Generating bezier handles based on constraints

I want to try to emulate what this application can do: Given the red round dots (from the mouse) it is able to solve for the bezier handles given that the tension of the curve is set to $0.6$. How ...
0
votes
0answers
57 views

Pick the right control point of a cubic bezier curve to form a part of a sinusoid

A,B,C,D are the control points of a Cubic Bézier Curve with approximately this shape: How do you pick point D (the last one, on the right) so that if you mirror the segment J-D of the curve ...
1
vote
1answer
53 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
2answers
221 views

Retrieve the initial cubic Bézier curve subdivided in two Bézier curves

I have a cubic Bezier curve subdivided to two cubic Bezier: Assuming that "t_cut" is the t value where this initial Bezier is cut: example of function subdivision(BezierCurve initialCurve, ...
0
votes
3answers
61 views

How to find 2 data point in Bezier satisfy the condition the Chord Length Method?

Suppose bezier curve have 4 control point $P0$, $P1$, $P2$, $P3$. How to find 2 data point $D1$, $D2$ satisfy the condition the Chord Length Method? The Chord Length Method : ...
1
vote
1answer
44 views

Question regarding Bezier Curve

A Bezier curve $Q$ has control points $P_0 = (0,0,0), P_1 = (0,1,0), P_2 = (1,1,0) and P_3 = (2,0,0)$. What point is $Q(\frac12)$?
0
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1answer
36 views

At what extent I can use trigonometric functions and properties with parametric curves?

I have a know-how and a library about trigonometry and trigonometric operations, I would like to know if I can possibly rely on trigonometry for parametric curves too and how the trigonometry from the ...
0
votes
1answer
73 views

What basis and coordinate system is used in this quadratic Bézier triangle equation? $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$

I have the following equation for a quadratic Bézier triangle, but I'm having a lot of trouble understanding how to describe it: $[x,y,z] = A*s^2 + B*t^2 + C*u^2 + D*2st + E*2tu + F*2su$ ...
1
vote
1answer
876 views

Calculate control points of cubic bezier curve approximating a part of a circle

I'm not mathematically inclined, so please be patient with my question. Given $(x_0, y_0)$ and $(x_1, y_1)$ as the endpoints of a cubic Bezier curve. $(c_x, c_y)$ and r as the centerpoint and the ...
0
votes
2answers
63 views

what is the parametric function of the new Bezier curve?

The cubic Bezier curve can be given in matrix form as If a cubic Bezier curve is rotated by an angle 30 around x-axis what is the parametric function of the new Bezier curve?
0
votes
1answer
83 views

Formula to derive angle and radius from Bezier circular curve control points

I know the x,y coordinates for the 2 endpoints and the 2 control points for a Bezier circular curve that is less than 180 degrees. I do not know the radius of the circle or the angle of the curve. ...
2
votes
1answer
120 views

Creating a surface from a path of 3D cubic bezier curves

I have a list of cubic bezier curves in 3D, such that the curves are connected to each other and closes a cycle. I am looking for a way to create a surface from the bezier curves. Eventually i want ...
1
vote
1answer
268 views

maximum curvature of 2D Cubic Bezier

Given a 2D cubic Bezier segment defined by P0, P1, P2, P3, here's what I want: A function that takes the segment and outputs the maximum curvature without using an iterative approach. I have a ...
1
vote
2answers
113 views

Fastest way to obtain the parametric value t of a bezier curve, for a given set x coordinates.

The problem is the following: Having a bezier curve B(t) we have coordinate x from the curve, and we need to obtain the y values from it, hence we need to compute the t values. What is the fastest ...
5
votes
1answer
154 views

Mathematical definition of Blender's F-Curves

I'm designing software for generating animation curves. I'd like the curves to be based on those found in Blender 3D, which they call "F-Curves." According to the page on the Blender Wiki, they are ...
0
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1answer
35 views

Points interpolation for tracking

I have set of points for ex. $A_0 (0,0); A_1 (1,2); A_3 (3,3);$ I need an object to travel between these points during some period of time. I was able to construct this trajectory with Bezier curve ...
3
votes
1answer
449 views

Understanding the Spiro Spline

My name's Wray. This is my first time here. Firstly, I like curves. I've been keeping a pet project for a long time that would implement a delightful new curve-interpolation algorithm named the Spiro ...
0
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1answer
84 views

Bezier curves, control points & reparameterization

Given a Bezier curve $\gamma$(t) defined by 3 control points P0 = (-1,4), P1 = (0, 0), P2 = (1, 0) such that the curve lies on the parabola $\ y = (x-1)^2 $. Reparameterize to $\alpha$(t) = ...
1
vote
1answer
152 views

Resample Bézier Curve with curvature and number of points constraints

I have an algorithm that implements an uniform resample process throughout a Bézier curve. This is done using a chord parametrization process. However, the results achieved do not accomplish my ...