# Tag Info

Accepted

### Computing a rotation: complex numbers vs rotation matrix

Both methods end up doing the same calculations when you break it down. Rotating a vector $u$ with a matrix: \begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{bmatrix} \...
Accepted

### How can I check if a polygon can completely contain a circle of a certain radius?

This is likely more complicated than you would prefer, but: Compute the medial axis, which immediately yields the largest disks that fit inside the polygon: their centers are vertices (degree $\ge 3$) ...
Accepted

### How to project a 3D point onto a plane along another (axis) vector?

You can determine x by calculating line-plane intersection. Your line starts at P and has direction ...

### How to build a 3d model from 2d pictures

This is a bit different from a conventional photogrammetry problem. You're not trying to estimate a 3D world from 2D projections. You have actual 3D information - you have the imaging slices - and you ...
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### Minimum requirements to uniquely represent a 3D object in space

A rigid body has 6 degrees of freedom, in 3D- space. So that means you need 6 values to represent the object. The common way to do this is to store a position vector for position and 3 rotations. But ...
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### results of Curved PN-Triangles algorithm has visible edges

As mentioned in the paper PN-triangles are only $C^0$ smooth with respect to adjacent triangles (although they are $G^1$ at vertices). This means that a PN triangle mesh is continuous in position, but ...
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### Apply distortion to Bézier surface

Edit: changed the answer according to new images and clarification. for every control point p(k, n) p'(k, n) = ( p(k, n) - p(k) ) * d * l(k) + p(k, n) where <...

### Computational Geometry - Triangulation

What it means to "triangulate complex 3D objects" is not unambiguous. Just one possible interpretation: You have a 3D polygon in space, and you want to triangulate that. This is NP-hard: Barequet, ...

### Reliable test for intersection of two Bezier curves

An alternative way to formulate the problem is to define a function that gives the distance between points on the two curves, as a function of the curves' parameters. Then attempt to find the global ...

### Reliable test for intersection of two Bezier curves

[Disclaimer: I think the following should work but have not actually coded it myself] I couldn't think of a "trivial" method of producing a yes/no answer but the following would be a reasonable ...
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### Convex non simple polygon?

For a polygon to be convex the outside angle of the polygon has to be more than or equal to 180 degrees. Now at intersection of 2 lines the outermost angle has to be less than 180 degrees for the ...

### How to describe a position of a point w.r.t the position and orientation of 3 other points

FYI, the 3 other points lie on a plane Of course they do. Any set of three points defines a plane (except in the degenerate case joojaa mentions, where they lie on many planes). If the points are $p$,...
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### What's the difference between geometric surface normal and shading surface normal?

Your existing opinion is correct, though there's one extra detail. The geometric normal is the normal of the actual triangle, based on the vertices' positions (the cross-product of edge vectors, as ...

### generate multiple border contour

Polygon offsetting is certainly possible to do yourself. It is not nearly as involved as Bezier or B-spline offsetting is. First you want to decide how to deal with: Areas with no info, in essence ...

### Best technique to draw overlapping colored line segments that follow the same route

This question should most probably be asked on GD.SE or UX.SE. These sites specialize in how to design the graphics and how to choose the graphics for your purpose. But since you are here basic ...

### File format for swept profile with changing normal

Well realistically your choices are either IGES or STEP. IGES is slightly simpler but you will not successfully write either format without buying the standard (which in case of step is actually so ...
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### Solving a set of Geometry Constraints - What's that Method called?

Its called a geometric constraints solver (a good primer on subject). You can find a open source solver as part of Open Cascade but its a bit convoluted to get going. A simpler solution for just ...
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### Can I run polygon insetting on the surface of a mesh?

This is more of a long comment Yes you can do this. The problem lies in how you measure the surface. I tried to do this manually by progressively extruding tubes along the edges, and finding their ...

### OpenGL with SFML, create an n-pointed star?

Try starting at the origin, then dividing 360 degrees by n to find some useful angles for the points of your star. I hope this drawing will help you to find a solution. Now that you have the angle ...