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.
198
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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 ...
- 561
15
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3
answers
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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 ...
- 82.4k
8
votes
2
answers
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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
...
- 1,894
21
votes
4
answers
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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 ...
- 82.4k
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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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7
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1
answer
155
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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 ...
- 114
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vote
2
answers
99
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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, ...
2
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3
answers
261
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Coordinates of spline plot using ArcLength mesh function
The following code produces a 3D spline with equidistant interpolation points:
...
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2
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294
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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
...
- 3,740
1
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1
answer
161
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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 ...
- 119
4
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2
answers
100
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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 ...
- 205
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2
answers
97
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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 ...
- 1,303
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0
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57
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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 ...
3
votes
2
answers
97
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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 ...
4
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1
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99
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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
...
- 23.1k
6
votes
1
answer
325
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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
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106
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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):
...
- 439
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161
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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 ...
- 11
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1
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449
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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 ...
- 5,672
6
votes
1
answer
849
views
Understanding Interpolation with Cubic Splines
My ultimate question: given data, what function is Interpolation with Method->"Spline" creating?
I recall from my ...
- 1,919
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2
answers
119
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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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276
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how to PiecewiseExpand BSplineBasis to get Basis matrices of uniform B-splines presented in the paper?
As we all know, the definition of B-spline contains the B-spline basis function, which has the recursive form
$B_{j,k}$ is the j-th degree $k-1$ polynomial. It has nonzeros only in interval $[t_j,t_{...
- 197
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0
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254
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NURBS model from a entire mesh
I have a mesh in STL file format and imported it into Mathematica.
data=Import["mesh.stl"];
or
...
- 39
4
votes
1
answer
144
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BSplineFunction returns unevaluated when its degree is equal to the number of control points
Bug fixed in 13.0.0 [CASE:4855260]
It seems that BSplineFunction always returns unevaluated without warnings, when its degree is equal to the number of control ...
- 62.1k
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388
views
7
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1
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146
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Texture prevents JoinedCurve from closing
Bug introduced in 11.3 or earlier and fixed in 12.1
I am running Mathematica 11.3 and would like to see if this behavior is still present in newer versions of Mathematica before submitting a bug ...
- 1,071
0
votes
0
answers
31
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Plot a quadratic bezier triangular patch [duplicate]
I need to construct a triangular patch by using the 6 control points:
$$\begin{array}{ccc}
\left(\frac{1}{2},\frac{\sqrt{3}}{4},1\right) & \left(\frac{1}{4},\frac{\sqrt{3}}{4},2\right) &
\...
- 31
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votes
1
answer
429
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Plot a bezier triangle
I have to construct a bezier triangle that interpolates these 4 points:
$\qquad (0,0,1),\,(1,0,0),\,(0,1,0),\,(0.5,0.5,0.75)$
However, the surface that I get is so weird. Anyone please can help me to ...
- 9
1
vote
2
answers
189
views
Access to Interpolation expression of Mathematica's Interpolate command
To reproduce fits which have been done in the framework of a standard, I was reviewing the Interpolation engine of Mathematica (for InterpolationOrder -> 3) to get more information about the ...
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12
votes
3
answers
456
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Why is there a discrepancy between JoinedCurve/FilledCurve and the underlying BSplineCurve segments?
This may be related to How to discretize a BezierCurve?, but this question deals with BSplineCurves with specific SplineWeights, ...
- 1,071
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0
answers
53
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Part::partw: error in Custom Spline Algorithm
I am attending a Calculus course where we use Wolfram as a supporting tool, and I was trying the algorithm provided for Spline interpolation and I get the error in the picture:
...
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5
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1
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254
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Find intersection points of arbitrary BSpline curve
I'm researching some computational geometry and am trying to find a method of determining the {x,y} intersection of a circle and BSplineCurve for further processing.
...
- 1,226
4
votes
1
answer
110
views
How can I control the length of the line segments used in rendering a BSplineCurve?
Mathematica seems to render rational Bézier curves (drawn with BSplineCurve) using polylines whose segments can be annoyingly long, while polynomial Bézier curves (...
- 561
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0
answers
109
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Export Basis spline information to matlab
i am new to Mathematica. I have generated the contours of this image with the following code
...
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1
answer
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Rendering PNG images to spline curves
I found something interesting on this page (Generic contour smoothing with shading) that could help me improve my images. Unfortunately, they can only be used with graphics generated by the software ...
- 9,263
4
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1
answer
151
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Why FilledCurve and BezierCurve or BSplineCurve do not fit
I want to draw the outline of a circle (it's actually the glyph period from Cascadia Code font):
...
- 235
9
votes
4
answers
1k
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Find smallest distance from a point to a Bézier curve
I wish to find the smallest distance from a point to a curved defined via a Bézier function. I want to do this automatically. For particular cases it is not to difficult. Here is a minimum working ...
- 16.6k
7
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1
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167
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How to draw a colored curved shape
I can draw a polygon with a curved edge using B-splines or Bézier curves:
...
- 1,048
2
votes
2
answers
251
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Best parameter for smoothing splines
I am trying to implement a module to determine the best value for the smoothing parameter of a smoothing spline interpolation of a given dataset. To calculate the cross-validation score of a given ...
- 435
5
votes
0
answers
112
views
Improving speed performance of 'Fit' with BSplines?
Context
In the context of this (vaguely controversial) question,
I am stumbling into a performance issue with Fit.
Let me illustrate on fitting a set of ...
- 23.1k
9
votes
0
answers
175
views
Dividing by Zero - Unexpected Result [closed]
When I divide this number by zero I get this for an answer.
ans = 2345900/0
(* *)
What is surprising is that in taking the square root, Mathematica seems to ...
- 7,193
6
votes
1
answer
579
views
Different results using spline interpolation in Wolfram and MATLAB
I use the same data for interpolation in Mathematica and MATLAB, but the result is different.
...
- 63
3
votes
2
answers
1k
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How to make a natural cubic spline of {{x,y}, ...} data
Consider
data = {{0, 0}, {1, 0}, {2, 0}, {3, 1}, {4, 0}, {5, 0}, {6, 0}};
f = Interpolation[data, InterpolationOrder -> 3, Method -> "Spline"];
Then the ...
- 7,144
5
votes
1
answer
81
views
Image artifacts while using BSplineCurve
Mathematica provides an example of visualizing a Hilbert curve using splines as a Graphics object in this entry in its documentation system.
However, when one attempts to change the thickness, some ...
2
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2
answers
214
views
Manual ArcLength sampling on spline differs from MeshFunction sampling
Using Michael E2's answer, I performed a manual arclength parameterisation by solving the differential equation (or: finding the inverse of a function whose derivative is known).
I compared the ...
- 123
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1
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144
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What are the automatic settings of a BSplineCurve object?
Consider the following object:
spline = BSplineCurve[{{0,1}, {1,1}, {0,1}, {-1,1}, {-1,0}}, SplineClosed->True];
Graphics[spline]
What would be an equivalent <...
- 131k
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votes
2
answers
155
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Find optimal BezierFunction
For a given set of points (examplary quadrant)
n = 5; (* number of inner points*)
p = Table[{Cos[φ], Sin[φ]}, {φ, Join[{0}, RandomReal[{0, Pi/2}, n], {Pi/2}]}];
...
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3
votes
3
answers
404
views
How to fit spline through points in $ \mathbb{R}^3$?
I have coordinates of points that represent a curve (for example, helix or centerline of moebius strip) in $ \mathbb{R^3}$. I want to fit a Bspline through these points. How to do this in Mathematica? ...
- 177
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votes
1
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130
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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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