Retrieving the Equasion of a Drawing - math

I'm looking into creating a web application trough witch the user could draw an arbitrary picture on a canvas (only lines involved, no fill and no different colors) and then obtain an equation witch graphs the same picture they've drawn. Does anybody has any idea on witch approach would be the most sensible one?
I thought about simply using Bézier curves to draw and then calculate it's equation, but I wanted to know if there's any other approach which might be more appropriate.

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Coloring the reverse side of mesh tiles in Scilab

In plot3d2 and similar graphic functions of Scilab, is there a way to set the colour of the back (reverse, flip, inner) side of facets?
I'm trying to draw a part of a (rather crude) torus, and the result is OK except for one row of facets. I suppose that, because of the way I generate the mesh, those facets are oriented differently - whatever algorithm renders them on the screen follows their perimeter in the opposite direction compared to others.
Instead of poring over my code to try to mend the topology of my mesh, I'd rather make sure the facet orientation doesn't matter - just set both sides to my colour. It will also improve the looks of the ends of my torus, where the inside shows and, again, is in a colour I didn't ask for.
But, hard as I search the documentation, I cannot find any mention of the flip side of mesh facets.
Any clues?
The backface color is named "hiddencolor" in the properties of a surface entity (see https://help.scilab.org/docs/6.1.1/en_US/surface_properties.html). It can be changed a posteriori, for example:
[X,Y]=meshgrid(-1:0.5:1);
plot3d2(X,Y,X.^2-2*Y.^2)
gce().hiddencolor=color("red")
You can assign -1 (instead of above) to use the same color as the front facing patches.
However, if all your patches are facing wrongly, you can also transpose all your matrices in the plot3d2 call:
[X,Y]=meshgrid(-1:0.5:1);
plot3d2(X',Y',(X.^2-2*Y.^2)')
gce().hiddencolor=color("red")

Cel shading/alpha shape in current visualization

I am playing around with rgl and I have created a 3D rendering of the mouse brain, in which structures can be isolated and coloured separately.
The original data is a 3D array containing evenly spaced voxels.
Every voxel is coded with a structure ID.
Every structure is rendered separately as a mesh by marching cubes, and smoothed using Laplacian smoothing as implemented by Rvcg.
Some of these structures can be quite small, and it would make sense to look at them within the context of the whole brain structure.
One of the options is to create a low-threshold mesh of the whole set of voxels, so that only the outer surface of the brain is included in the mesh.
This surface can be smoothed and represented using a low alpha in rgl::shade3d colouring faces. This however seems to be quite taxing for the viewport as it slows down rotation etc especially when alpha levels are quite low.
I was wondering if there is any way to implement some sort of cel shading in rgl, e.g. outlining in solid colours the alpha hull of the 2D projection to the viewport in real time.
In case my description was not clear, here's a photoshopped example of what I'd need.
Ideally I would not render the gray transparent shell, only the outline.
Cel shading example
Does anybody know how to do that without getting deep into OpenGL?
Rendering transparent surfaces is slow because OpenGL requires the triangles making them up to be sorted from back to front. The sort order changes as you rotate, so you'll be doing a lot of sorting.
I can't think of any fast way to render the outline you want. One thing that might work given that you are starting from evenly spaced voxels is to render the outside surface using front="points", back="points", size = 1. Doing this with the ?surface3d example gives this fake transparency:
If that's not transparent enough, you might be able to improve it by getting rid of lighting (lit = FALSE), plotting in a colour close to the background (color = "gray90"), or some other thing like that. Doing both of those gives this:
You may also be able to cull your data so the surface has fewer vertices.

How to Minimize the saved points from drawn points using free-flow drawing tool

Currently I'm using "Douglas Peucker" algorithm.
My problem is that when I'm drawing,the previously drawn lines are also changing which of course not realistic. Is there other alternative algorithm to minimize the saved points but not altering the previous drawn points or other way to alter "Douglas Peucker" to fit my need?
Give your pencil drawing tool 2 optional methods for drawing:
Draw a new point on the path using mousemove (which is your current freeform method). This option will let the user add many points which will allow them to be very detailed in their drawing.
Draw a new point on the path only upon mousedown. This option simply connects the previous point on the path to the newly clicked point. This option will let the user add just a few very straight lines which will allow them to outline figures with long running straight edges.
If you are concerned about the freeform path changing while the user is drawing you can apply the simplifying algorithm just once after they have stopped moving the mouse for 1 second.
If you specify the Douglas-Peucker algorithm use a high bias for accuracy then the simplified path will remain quite true to the unsimplified path.
BTW, if you want to draw splines through your points then check out this nice previous post: how to draw smooth curve through N points using javascript HTML5 canvas?

Map 3D point cloud onto surface then flatten

Mapping a point cloud onto a 3D "fabric" then flattening.
So I have a scientific dataset consisting of a point cloud in 3D, this point cloud comprises points on a surface that is curved. In order to perform quantitative analysis I however need to map these point clouds onto a surface I can then flatten. I thought about using mapping tools sort of like in the case of the 3d world being flattened onto a map, but not sure how to even begin as I have no experience in cartography and maybe I'm trying to solve an easy problem with the wrong tools.
Just to briefly describe the dataset: imagine entirely transparent curtains on the window with small dots on them, if I could use that dot pattern to fit the material the dots are on I could then "straighten" it and do meaningful analysis on the spread of the dots. I'm guessing the procedure would be to first manually fit the "sheet" onto the point cloud data by using contours or something along those lines then flattening the sheet thus putting the points into a 2d array. Ultimately I'll probably also reduce that into a 1D but I assume I need the intermediate 2D step as the length of the 2nd dimension is variable (i.e. one end of the sheet is shorter than the other but still corresponds to the same position in terms of contours) I'm using Matlab and Amira though I'm always happy to learn new tools!
Any advice or hints how to approach are much appreciated!
You can use a space filling curve to reduce the 3d complexity to a 1d complexity. I use a hilbert curve to index lat-lng pairs on a 2d map. You can do the same with a 3d space but it's easier to start with a simple curve for example a z morton order curve. Space filling curves are often used in mapping applications. A space filling curve also adds some proximity information and a new sort order to the 3d points.
You can try to build a surface that approximates your dataset, then unfold the surface with the points you want. Solid3dtech.com has the tool to unfold the surfaces with the curves or points.

Disperse points in a 2D visualisation

I have a set of points like this (that I have clustered using R):
180.06576696, 192.64378568
180.11529253999998, 192.62311824
180.12106092, 191.78020965999997
180.15299478, 192.56909828000002
180.2260287, 192.55455869999997
These points are dispersed around a center point or centroid.
The problem is that the points are very close together and are, thus, difficult to see.
So, how do I move the points apart so that I can distinguish each point more clearly?
Thanks,
s
Maybe I'm overlooking some intricacy here, but...multiply by 10?
EDIT
Assuming the data you listed above are Cartesian (x,y) coordinate pairs, you can visualize them as a scatter plot using Google Charts. I've rounded your data to 3 decimal places, because Google Charts doesn't appear to handle higher precision than that.
I don't know the coordinates for your central point. In the above chart, I'm assuming it is somewhere nearby and not at (0,0). If it is at (0,0), then I imagine it will be difficult to visualize all of the data at once without some kind of "zoom-in" feature, scaling the data, or a very large screen.
slotishtype, without going into code, I think you first need to add in the following tweaking parameters to be used by the visualization code.
Given an x by y display box, fill the entire box, with input parameters [0.0 to 1.0]...
overlap: the allowance for points to be placed on top of each other
completeness: how important is it to display all of your data points
centroid_display: how important is it to see the centroid in the same output
These produce the dependent parameter
scale: the ratio between display distances to numerical distances
You will need code to
calculate the distance(s) to the centroid like you said,
and also the distances between data points, affecting the output based on the chosen input parameters.
I take inspiration from the fundamentals in the GraphViz dot manual. Look at the "Drawing Orientation, Size and Spacing" on p12.

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