# Questions tagged [splines]

Questions on the spline-related functions of Mathematica (BezierCurve[], BSplineCurve[], etc.), or related to the theory and use of splines in Mathematica.

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### Can I make rendering of BSplineCurves more accurate?

My gently curving BSplines are being rendered as straight lines that are long enough to look bad. As an example, consider drawing a dartboard, with its twenty colored sectors. The outer boundaries ...
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### Edna Andrade's Black Dragon: Winding Around Control Points

Edna Andrade Edna Andrade (1917-2008) is now recognized as an early leader in the Op Art movement. She lived and worked in Philadelphia for the majority of her career after first moving to the city ...
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### How to make Region from Spline curve

Let bsf = BSplineFunction[{{1, 1}, {-0.5, -0.7}, {-0.4, -1}, {1, 0}}, SplineClosed -> True, SplineDegree -> 3] Than ...
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### Paul Klee's Notebooks: Loops Around Control Points

Paul Klee Paul Klee (1879 - 1940) was a Swiss-born German artist. His highly individual style was influenced by expressionism, cubism, and surrealism. Klee was a natural draftsman who deeply explored ...
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1 vote
60 views

### Replacing Terms of a Table of Functions

I define a table of functions, and I receive and error when I want to change a term of the table. As a minimal example, I can give the following. ...
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### Creating a Random T-Spline Instead of a B-Spline

I want to be able to create a function so that instead of BSplineSurface[pts], it would be TSplineSurface[pts,error]. I think it ...
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1 vote
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### Positive Change, Negative Change, and Total Change with Values on Graph

I am trying to show a change in cross-section geometry between years, and have good visual plots but would like actual values to use also. I am using spline curves to visualize the cross sections, ...
261 views

### Coordinates of spline plot using ArcLength mesh function

The following code produces a 3D spline with equidistant interpolation points: ...
294 views

### What do the arguments of a generated BSplineFunction mean?

For example, if we evaluate this: BSplineFunction@{{0,100},{200,50},{200,0}} we'll get ...
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1 vote
161 views

### Proper way to discretize a parametric spline surface

Given that I have a triangular mesh model defined in obj format (1590 vertices and 300 faces), I reconstruct it to a single B-spline surface. Now I want to export ...
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### How to integrate 2 compoonent spline function

I have a Spline function defined as follows. Points = {{0, 0}, {0, 1}, {1, 1}, {1, 0}, {0, 0}}; bsf = BSplineFunction[Points, SplineDegree -> 1]; A Parametric ...
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### Options to find an analytical description of some points

I have a set of points {{x1,y1},...{xn,yn}} and I would like to have the analytical expression of a function that describes them reasonably well. So that I can plot this function on a ...
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### Getting Log10 axis in Graphics Function

In the output shown in the following image, I need x axis to be logarithmic (base 10) instead of linear. When I used ListLogLinearPlot function I got scattered points instead of the required B Spline ...
97 views

### How to NIntegrate multiple ranges of data at the same time with an output that can be plotted?

I am trying to use the NIntegrate function to find the difference in the area beneath two 2 dimensional splines (how much area of the river bed was lost or gained from one year to the next) but, I ...
99 views

### CaputoD of (Edge) BSplines

tl;dr Why does this works: CaputoD[BSplineBasis[{3, {0, 1, 2, 3, 4}}, 0, x], {x, 1/2}] // Simplify Whereas this fails ...
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### Convert interpolating function to a Bezier curve

I've been wondering, is there a way to convert an interpolation into a sequence of BezierCurve objects that form each step in the interpolation? There is an easy ...
• 241k
1 vote
106 views

### Recurrence relation for B-spline polynomials

I am trying to get the explicit polynomials of cardinal B-splines. So far I have this implementation (for cardial B-splines of degree 3 on the knots 0, 1, 2, 3): ...
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1 vote
161 views

### How does Mathematica's B-Spline NURBS work?

I'm finding that Mathematica is getting hung up on a numerical integration and I suspect I can do it faster myself in C++. I can scoop the control points of the BSplineFunction out of the ...
449 views

### Geogebra spline command in Mathematica

Spline(pts, order, Weight Function) Creates a spline with given order through all points. The weight function says what should be the difference of t values for point $P_i$ and $P_{(i+1)}$ given ...
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### Understanding Interpolation with Cubic Splines

My ultimate question: given data, what function is Interpolation with Method->"Spline" creating? I recall from my ...
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1 vote
119 views

### Is task to find intersections of a line and a cubic Bezier curve really so hard?

I wrote formulas for parametric Bezier curves of different orders ...
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### How to construct BezierFunction for BezierCurve with npts>4 and SplineDegree -> 3?

I would like to use BezierCurve with npts=7 and SplineDegree -> 3 and access its BezierFunction. This code helps: ...
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