# Questions tagged [curve]

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### How to remove a control point from a NURBS curve?

I am trying to write an algorithm to remove a control point from a NURBS curve, similarly to what can be achieved using the CVREMOVE command in AutoCAD. I searched online but I was unable to find a ...
857 views

### Rendering splines on GPU

We have an application which needs to render spline curves (cubic, bezier, b-spline etc.). We currently have working algorithms in C to stroke the control points of these curves into line strips. The ...
583 views

### Fake cubic Hermite spline interpolation with smoothstep

When scaling an image with Bicubic Interpolation, the Cubic Hermite spline interpolation is used. smoothstep is one of the four basis/blend functions of this kind ...
286 views

### How to get coordinates of mouse after left mouse button is released after drag in OpenGL?

I want to get the coordinates of my mouse after the left mouse button is released after being dragged in OpenGL? I am new to this and wanted to know how I can implement it.
1k views

### Continuity of parametric and geometric continuity

We know that in parametric continuity, $C^1$ continuity is two successive curve section $C_1$ and $C_2$ has first parametric derivative is same. That means tangent vector $t_1$ is same for both $C_1$ ...
1 vote
1k views

### Spline interpolation library in cpp

Have been searching a lot for a good spline interpolation library in cpp, came across one, which is the famous Eigen library , having the unsupported counterpart for spline fitting.<Here>. I ...
1 vote
175 views

### How does the Lane Riesenfeld algorithm work?

I understand de Casteljau's algorithm and I am familiar although not fully experienced with B-Splines. I am trying to understand the geometric interpretation of B-splines through the algorithm (just ...
1 vote
2k views

### How to take the derivative of a Bézier curve?

I want to know how to take the derivative of a Bézier curve. I visited this website https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/Bezier/bezier-der.html, but I am unable to figure out how ...
157 views

### How do you compute the winding number of a closed poly curve?

Pretty much the title, given a closed curve in 2D, defined by a set of points, and a point. What's the algorithm to calculate the winding number of that curve, point pair?
631 views

### Conversion from cubic catmull-rom spline to cubic b-spline

I have a bunch of points that are the control vertices of a cubic catmull-rom spline. I would like to convert these to the control vertices of a cubic bspline. I believe I can do this using this ...
535 views

### Determining Rational Quadratic Bezier Curve Weights for Circle

I am trying to create a spherical interpolation with 3 points. I'm currently using Quadratic Bezier Interpolation but have been told I should use Rational Quadratic Bezier Curve in order to get a ...
219 views

### How do people come up with subdivision schemes?

Be it chaikin subdivision, loop subdivision, catmull-clark subdivision... How do people come up with the coefficients for an arbitrary subdivision scheme?
163 views

### Projecting one Quadratic Bezier Curve Onto Another

I'm working on improving an open source rasterization library called Gudni that I started a few years ago. It's source repository and the branch I'm currently working on are here: https://github.com/...
345 views

### Non least squares formulation to fit catmull rom spline

I have a set of unordered points that I'm getting from an image attached. I'd like to simply fit a parametrized curve such as a catmull-rom curve to with n control points (n = 4 to 10, and can be ...
123 views

### Why cubic curves provide the minimum curvature interpolants?

As described by Shirley in his computer graphics book, Cubic curves provide the minimum-curvature interpolants to a set of points. That is, if you have a set of n + 3 points and define the “...
274 views

### If you can use subdivision surfaces for 2D curves

I've seen how subdivision surfaces are good for 3D curves/modeling, but haven't seen anything on if it's good, or even usable, in 2D. My question is just that, if (a) you can even use subdivision ...
1 vote
306 views

### How should I generate Kochanek-Bartels spline endpoints?

I'm working on a program which uses Kochanek-Bartels ("TCB") splines. My question is: How do I deal with the first/last points of the spline? This type of spline needs a 'previous' and 'next' point ...
1 vote
2k views

### B spline curve generation in Python

I am using the de boors algorithm to generate B splines in python. However I am getting spikes in the final figure. I do not understand why this happens. I am posting my code here for reference <...
236 views

### Midpoint Algorithm Fast Direction

I've been exploring the Midpoint algorithm for drawing lines and curves, and I have a quick question: How should you determine the fast direction for a curve? I've seen that if the shape is simple, ...
1 vote
40 views

### Program to visualize geodesics and linear projection of an ellipsoid simultaneously

I am trying to solve a problem in computer graphics but to do it I need to be able to see a comparison of geodesic lines and straigth line projections on the ellipsoid. I have not been able to ...
326 views

### Polygons versus curve primitives in software rendering

Most 3D video games since the nineties have used hardware rendering based on polygons. Why polygons? They work well for some things, but not so well for others, e.g. a human figure rendered in ...
109 views

### Does the blending matrix change between calculating various curve segments in a uniform cubic B-splines approximation?

I would like to ask about uniform (periodic) cubic B-splines (approximation, no interpolation). B=1/6\begin{bmatrix}-1&3&-3&1\\3&-6&3&0\\-3&0&3&0\\1&4&1&...
504 views

### How to use Monotone cubic interpolation in 3D?

I wanted to use Monotone cubic interpolation, but the site only provide explanation for 2D case. How can I extend it to 3D?
180 views

### Move position in smooth gradient

I am decrementing/incrementing position x until it reaches y. However, this creates a rectangular-like path. I want position x to smoothly curve towards y (diagonally) on a 2D plane. What kind of ...
3k views

### How to deform some mesh so that it fits along a spline curve? [closed]

Given a set of vertices, transforming them to fit onto some spline curve. For example 3D modelling software has extrude along curve and Unreal Engine has a spline mesh component that takes some mesh ...
1 vote
304 views

### Curves fairness

Curves fairness is a strange problem in Computer Aided Geometric Design and every author gives his personal definition. One of the simplest is the following: A curve is said to be fair if (1) it is ...
282 views

### Converting raster shape/blob into displacement map

I am a beginner in digital image processing and computer graphics. I would like to program a similar behavior than the Shadermap 3 normal editor (displacement layer more specifically). As shown in ...
3k views

### Ordering a set of unorganized points along a curve

I have a set of 3D points (which I recover from a library that performs the tessellation of a solid body) that belong to a curve (i.e., an edge of the solid). That means that the curve surely passes ...
1k views

### How to calculate matching roundness of two offset rectangles?

I have two rectangles — one with a fill (blue) and one with a stroke (red). The red rectangle is being offset (depending on the stroke width) so that it appears snug and outside the edge of the blue ...
2k views

### Is there some kind of Bresenham algorithm or equivalent for scanline rendering a rotated ellipse?

Back in the day when you often had to write your own low level rendering algorithms we all used to learn the Bresenham algorithms for lines and circles. It was almost trivially easy to extend the ...