I've successfully calibrated my camera and I can get the dimensions of a XLD in world coordinates with ContourToWorldPlaneXld and then HeightWidthRatioXld. This returns me the measures of a contour extracted from a shape.
Now I need to convert a value inserted by the user in mm (example in mm: 0.1) and get how many pixels the measure is, for example, to draw a line.
I need the pixel value as per request. I tried looking around in the Halcon documentation but I didn't find what I was looking for.
Also I read this answer but it' not exactly what I'm looking for.
I'm using Halcon Progress 21.11.
Edit: A possible solution could be obtaining the dimensions before converting them to world plane and then do something like pixel/world but I would prefer a better method if it exists.
So I was reading a Document about Displacement Mappings and Surface Blendings and came across this equation which is supposed to be a Alpha-Blending equation:
while v1,...,vn are supposed to be the value vector and w1,....,wn the weight vector (is how the document describes it).
To tell what my interpretation of this equation is, is that considering n being the number of surfaces we are trying to blend together the value vectors are supposed to represent as the name says the value (probably color related?) of each surface and the weight vector basically describing the value preference of each surface (so the higher the weight value the more we would see the color of that one surface after the blend). The multiplication and division part is something what i do not fully understand (just interpreting it as the 'it just works like that' part of the equation)
I couldn't find any similar equation anywhere so far so I figured out that either I didn't search deep enough or I am not understanding something that is supposed to be very obvious and I wanted to make sure that fully understand this equation for further read in the document which bases on this idea.
I am currently creating a feature and patterning it across a flat plane to get the maximum number of features to fit on the plane. I do this frequently enough to warrant building some sort of marcro for this if possible. The issue that I run into is I still have to manually set the spacing between the parts. I want to be able to create a feature and have it determine "best" fit spacing given an area while avoiding overlaps. I have had very little luck finding any resources describing this. Any information or links to potentially helpful resources on this would be much appreciated!
Thank you.
Before, you start the linear pattern bit:
Select the face2 of that feature2, get the outer most loop2 of edges. You can test for that using loop2.IsOuter.
Now:
if the loop has one edge: that means it's a circle and the spacing must superior to the circle's radius
if the loop has more that one edge, that you need to calculate all the distances between the vertices and assume that the largest distance is the safest spacing.
NOTA: If one of the edges is a spline, then you need a different strategy:
You would need to convert the face into a sketch and finds the coordinates of that spline to calculate the highest distances.
Example: The distance between the edges is lower than the distance between summit of the splines. If the linear pattern has the a vertical direction, then spacing has to be superior to the distance between the summit.
When I say distance, I mean the distance projected on the linear pattern direction.
Say I want to construct a 3D cubic Bézier curve, and I already have both end-points, and the direction (normal vector) for both control points. How can I choose the distance of both control points to their respective end-points in order to make the curve as 'nicely rounded' as possible?
To formalize 'nicely rounded': I think that means maximizing the smallest angle between any two segments in the curve. For example, having end-points (10, 0, 0) and (0, 10, 0) with respective normal vectors (0, 1, 0) and (1, 0, 0) should result in a 90° circular arc. For the specific case of 2D circular arcs, I've found articles like this one. But I haven't been able to find anything for my more general case.
(Note that these images are just to illustrate the 'roundness' concept. My curves are not guaranteed to be plane-aligned. I may replace the images later to better illustrate that point.)
This is a question of aesthetics, and if the real solution is unknown or too complicated, I would be happy with a reasonable approximation. My current approximation is too simplistic: choosing half the distance between the two end-points for both control point distances. Someone more familiar with the math will probably be able to come up with something better.
(PS: This is for open-source software, and I would be happy to give credit on GitHub.)
Edit: Here are some other images to illustrate a 3D case (jsfiddle):
Edit 2: Here's a screenshot of an unstable version of ApiNATOMY to give you an idea of what I'm trying to do. I'm creating 3D tubes to represent blood-vessels, connecting different parts of an anatomical schematic:
(They won't let me put in a jsfiddle link if I don't include code...)
What you are basically asking is to have curvature over the spline as constant as possible.
A curve with constant curvature is just a circular arc, so it makes sense to try to fit such an arc to your input parameters. In 2D, this is easy: construct the line which goes through your starting point and is orthogonal to the desired direction vector. Do the same for the ending point. Now intersect these two lines: the result is the center of the circle which passes through the two points with the desired direction vectors.
In your example, this intersection point would just be (0,0), and the desired circular arc lies on the unit circle.
So this gives you a circular arc, which you can either use directly or use the approximation algorithm which you have already cited.
This breaks down when the two direction vectors are collinear, so you'd have to fudge it a bit if this ever comes up. If they point at each other, you can simply use a straight line.
In 3D, the same construction gives you two planes passing through the end points. Intersect these, and you get a line; on this line, choose the point which minimizes the sum of squared distances to the two points. This gives you the center of a sphere which touches both end points, and now you can simply work in the plane spanned by these three points and proceed as in 2D.
For the special case where your two end points and the two known normal vector for the control points happen to make the Bezier curve a planar one, then basically you are looking for a cubic Bezier curve that can well approximate a circular arc. For this special case, you can set the distance (denoted as L) between the control point and their respective end point as L = (4/3)*tan(A/4) where A is the angle of the circular arc.
For the general 3D case, perhaps you can apply the same formula as:
compute the angle between the two normal vectors.
use L=(4/3)*tan(A/4) to decide the location of your control points.
if your normals are aligned in a plane
What you're basically doing here is creating an elliptical arc, in 3D, where the "it's in 3D" part is completely irrelevant, since it's just a 2D curve, rotated/translated to sit in your 3D space. So let's just solve the 2D case, and then the RT is entirely up to you.
Creating the "perfect" cubic Bezier between two points on an arc comes with limitations. You basically can't create good looking arcs that span more than a quarter circle. So, with that said: your start and end point normals give you a 2D angle between your normal vectors, which is the same angle as between your start and end tangents (since normals are perpendicular to tangents). So, let's:
align our curve so that the tangent at the start is 0
plug the angle between tangents into the formula given in the section on Circle approximation in the Primer on Bezier curves. This is basically just dumb "implementing the formula for c1x/c1y/c2x/c2y as a function that takes an angle as argument, and spits out four values as c1(x,y) and c2(x,y) coordinats".
There is no step 3, we're done.
After step 2, you have your control points in 2D to create the most circular arc between a start and end point. Now you just need to scale/rotate/translate it in 3D so that it lines up with where you needed your start and end point to begin with.
if your normals are not aligned in a plane
Now we have a problem, although one that we can deal with by treating the dimensions as separate things entirely. Instead of creating a single 2D curve, we're going to create three: one that's the X/Y projection, one that's the X/Z projection, and one that's the Y/Z projection. For all three of these, we're going to abstract the control points in exactly the same way as before, and then we simply take the projective control points (three for each control point), and then go "okay, we now have X, Y, and Z projective coordinates. That means we have (X,Y,Z) coordinates", and done again.
Does anyone have any ideas how to implement a monte carlo integration simulator in vb.net.
I have looked around the internet with no luck.
Any code, or ideas as to how to start it would be of help.
Well i guess we are talking about a 2 dimensional problem. I assume you have a polygon of which you want to calculate the area.
1) First you need a function to check if a point is inside the polygon.
2) Now you define an area with a known size around the polygon.
3) Now you need random points inside your known area, some of them will be in your polygon, some will be outside, count them!
4) Now you have two relations: First the relations of all points to points inside your polygon. Second the area around your polygon which you know, to the area of the polygon you don't know.
5) The relations is the same --> you can calculate the area of your polygon! (Area of polygon should be: points in you polygon / all your points * size of known area)
Example: 3 points hits hit the polygon, 20 points where "shot", the area of the polygon is 0.6m²
NOTE: This area is only an approach! The more points you have, the better the approach gets.
You can implement a fancy method to display this in your vb program of course. Was this what you needed? Is my assumption about the polygon correct? Do you need help with the "point inside polygon" algorithm?
There is nothing specific to VB.net with this problem, except maybe for the choice of a random number generator from the library.
Numerically solving integrals of a function f(x_1,...,x_n) by using can become infeasible (in acceptable time) for high dimensions n, because the number of sample points needed for a given sampling distance grows exponentially with the dimension of the problem. The fundamental idea with Monte Carlo Integration is to replace the uniform sampling of the variables x_1,...,x_n with random sampling, taking n random numbers per sample. With these samples, estimate the integral. The more samples, the better the estimate. And the major benefit of MC integration is, that you can use standard statistical methods to estimate the error of your result.
So, how to start: Implement integration by uniform sampling of the integration space, then go to random sampling and add error estimation.