0
votes
1answer
23 views

Plane fitting using svd

I am trying to get a best fit plane in a 3d space of points. I am using an svd as described in http://stackoverflow.com/questions/10900141/fast-plane-fitting-to-many-points. If I use the data provided ...
8
votes
2answers
227 views

General method to “naturally interpolate” to a complex map?

Given a region of the complex plane and a map $z \to f(z)$, is there a general way to "naturally interpolate" the point $z$ to $f(z)$ in such a way that the movement follows a "natural" smooth path ...
0
votes
0answers
17 views

How to find the tangents for a spiral geometry at each point accurately

I have been working on a progam that generates spirals from contours that have been formed by slicing a surface by various planes along its height.The contours are a collection of linear line ...
0
votes
1answer
37 views

Defined matrix in Catmull Spline Curve

I am trying to use Catmull spline curve in my program , I am trying to understand it but why we only use below given Matrix , because the examples I saw I only found the below one In Catmull spline ...
0
votes
1answer
42 views

Solving sub-triangles for Barycentric Interpolation (Triangle Geometry)

I'm trying to solve this triangle, so I can implement a barycentric interpolation, but I'm having trouble solving everything. I have all the base values for each of triangular sections and with a ...
1
vote
1answer
92 views

Catmull-Rom blending functions

I have a non-uniform Catmull-Rom spline (so the $t_i$ parameter values are not uniformly distributed). Is there a simple way to calculate the blending functions of the control points? So the spline ...
0
votes
1answer
122 views

Interpolating geographic coordinates

I have two geographic coordinates. Let's call them $A$ and $B$: A = latitude 41.34759, longitude -75.77415 B = latitude 41.34769, longitude -75.77404 My unknown ...
0
votes
1answer
70 views

Linear interpolation of rotations

To linearly interpolate between two points $p_1$ and $p_2$ in 3-space, I can calculate: $p_t = p_1 + t(p_2-p_1)$ where $t$ is a parameter $0 <= t <= 1$ Is there any representation of rotation ...
1
vote
0answers
83 views

Quaternion barycentric interpolation

Let's say that i have a set of quaternions, each representing a 3-angle orientation. And with each quaternion is associated a real value (let's say a speed value for explanation's sake). Now with an ...
2
votes
0answers
117 views

monotonic smoothing fit to be implemented (in python or other language)

In a post that already exists, implementation-of-monotone-cubic-interpolation, there is a good method for fitting data which necessarily includes all of the given points. But, what if I need to ...
2
votes
0answers
76 views

Minimal surface representation from a 3D contour

I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane and I want to obtain a 3D triangular mesh representation of the surface inside ...
0
votes
2answers
111 views

Finding t in basic geometric interpolation

I have the following problem related to interpolation and was wondering if anyone had any ideas? In the following diagram, there exists known-points: A, B, C, D, E, unknown points F, G. I'm trying ...
3
votes
1answer
74 views

Linear, Bi-linear or better

I have been writing some code to do some interpolation of 2D data on an irregular grid. So far what I have done is: Triangulate the known points using Delaunay. Find the vertices of the triangles ...
4
votes
2answers
147 views

How to make 3D object smooth?

I want to make the below picture into an egg with smooth surface. For the implementation in Mathematica, please, see this thread here. This thread considers mathematical methods to achieve the goal ...
2
votes
1answer
126 views

A Question About Linear Interpolation

So lets say I have two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. $A$ and $B$ are each associated with some scalar value $K_1$ and $K_2$. $K_1$ is negative and $K_2$ is positive and all the ...
1
vote
2answers
65 views

What is the equation stands for in geometry(intuitively)?

I am writing a bilinear interpolation method. This method can be abstract by solve the equation A*x = b, A is a 4x4 matrix below: $A=\begin{pmatrix} 1 &x_1 &y_1 &x_1y_1\\ 1 ...
0
votes
1answer
145 views

Closest edge to a point

I have a tricky question and can't seem to find a good solution. Let's say I have 3 convex polygons (ABCD, ADEF, BHGC) that share 2 common edges, unknown J, and a known point I: I want to find the ...
0
votes
2answers
85 views

Interpolating point outside quad

I'm trying to interpolate a destination point $(x,y)$ outside of a $4$ point convex polygon given a $4$ point source polygon with known values. It's sort of like inverse bilinear interpolation, except ...
0
votes
3answers
106 views

Which Interpolation should I use to create a curve?

I'm pretty weak in the field of mathematics, but a strong programmer. I am looking for a mathematical solution that, given two points on a line will give me a curve between them, including those two ...
0
votes
0answers
133 views

How do I create a shape from a square corners' values?

I'm working on a 3D algorithm, so my problem applies to cubes, not squares. But for convenience, I'll stick to 2D. Each corner of a square can contain up to 100 units, depending of the values at each ...
1
vote
0answers
75 views

Questions about interpolating translated points from a grid

I would like to do the following transformations on a very low resolution bitmap (64x64 pixels). I am doing this transformation on a computer images, but it has nothing to do with computers, you can ...
1
vote
1answer
42 views

Equally distributing cards on a table. (interpolation)

this problem is originally from a programming task i am on. there is a number of playing cards n. the width of each card is w. now the cards should be placed next to each other on a table with equal ...
2
votes
3answers
229 views

creating smooth curves with f(0) = 0 and f(1) = 1

I would like to create smooth curves, which have f(0) = 0 and f(1) = 1. What I would like to create are curves similar to the gamma curves known from CRT monitors. I don't know any better way to ...
1
vote
1answer
152 views

Decomposition of any point in the unit hypercube as a positive linear combination of polynomial number of vertices

I have function values at each of the vertices of the hyper cube. What would be a natural interpolation of the function to each point on and inside the cube that can be written as a positive linear ...
3
votes
2answers
3k views

Implementation of Monotone Cubic Interpolation

I'm in need to implement Monotone Cubic Interpolation for interpolate a sequence of points. The information I have about the points are x,y and timestamp. I'm much more an IT guy rather than a ...