I am using Dundas Maps and attempting to draw a map of the world where countries are grouped into regions that are specific to a business implementation. I have shape data (points and segments) for each country in the world. I can combine countries into regions by adding all points and segments for countries within a region to a new reg...
I have a quadratic bezier curve described as (startX, startY) to (anchorX, anchorY) and using a control point (controlX, controlY). I have two questions: (1) I want to determine y points on that curve based on an x point. (2) Then, given a line-segment on my bezier (defined by two intermediary points on my bezier curve (startX', start...
Greetings, I'm working on a game project that uses a 3D variant of hexagonal tile maps. Tiles are actually cubes, not hexes, but are laid out just like hexes (because a square can be turned to a cube to extrapolate from 2D to 3D, but there is no 3D version of a hex). Rather than a verbose description, here goes an example of a 4x4x4 map...
Hello: I have a unit vector in 3D space whose direction I wish to perturb by some angle within the range 0 to theta, with the position of the vector remaining the same. What is a way I can accomplish this? Thanks. EDIT: After thinking about the way I posed the question, it seems to be a bit too general. I'll attempt to make it more sp...
Does anyone know of a good (efficient, nice API, etc.) geometry open source library for .NET? Some of the operations needed: Data Structures Vectors (2D and 3D with floats and doubles) Lines (2D and 3D) Rectangles / Squares / Cubes / Boxes Spheres / Circles N-Sided Polygon Matrices (floats and doubles) Algorithms Intersection calcu...
There is a very handy set of 2d geometry utilities here. The angleBetweenLines has a problem, though. The result is always positive. I need to detect both positive and negative angles, so if one line is 15 degrees "above" or "below" the other line, the shape obviously looks different. The configuration I have is that one line remains s...
Given two polygons: POLYGON((1 0, 1 8, 6 4, 1 0)) POLYGON((4 1, 3 5, 4 9, 9 5, 4 1),(4 5, 5 7, 6 7, 4 4, 4 5)) How can I calculate the union (combined polygon)? Dave's example uses SQL server to produce the union, but I need to accomplish the same in code. I'm looking for a mathematical formula or code example in any language that ...
Hello: I would like to generate random points on a 3D box defined by its (minx, miny, minz) and (maxx, maxy, maxz) corners. I was thinking of generating a random point inside of the box and then somehow projecting it onto one of the box sides. However, I don't have explicit plane information for the box sides and this seems like it will...
Just wondering if there was a nice (already implemented/documented) algorithm to do the following Given any shape (without crossing edges) and two points inside that shape, compute all the paths between the two points such that all reflections are perfect reflections. The path lengths should be limited to a certain length otherwise ther...
Hi everyone, I'm searching for an algorithm to calculate the average distance between a point and a line segment in 3D. So given two points A(x1, y1, z1) and B(x2, y2, z2) that represent line segment AB, and a third point C(x3, y3, z3), what is the average distance between each point on AB to point C? I'm also interested in the averag...
Project a cubic bezier p1,p2,p3,p4 onto the line p1,p4. When p2 or p3 does not project onto the line segment between p1 and p4, the curve will bulge out from the anchor points. Is there a way to calculate the T value where the tangent of the curve is perpendicular to the anchor line? This could also be stated as finding the T values w...
In industry, there is often a problem where you need to calculate the most efficient use of material, be it fabric, wood, metal etc. So the starting point is X amount of shapes of given dimensions, made out of polygons and/or curved lines, and target is another polygon of given dimensions. I assume many of the current CAM suites implem...
Hello: I wish to randomly and uniformly generate points on a cylinder and a cone (separately). The cylinder is defined by its center, its radius and height. Same specifications for the cone. I am able to get the bounding box for each shape so I was thinking of generating points within the bounding box. However, I'm not sure how to proje...
Hi, Consider the following problem - I am given 2 links of length L0 and L1. P0 is the point that the first link starts at and P1 is the point that I want the end of second link to be at in 3-D space. I am supposed to write a function that should take in these 3-D points (P0 and P1) as inputs and should find all configurations of the li...
Given a cubic bezier curve P0,P1,P2,P3 with the following properties: Both P1 and P2 are on the same side of the line formed by P0 and P3. P2 can be projected onto the line segment formed by P0 and P3 but P1 cannot. What is the T value for the point on the curve farthest from P3? Here is an image with an example curve. The curve bu...
Hopefully there are some computational geometry folks here who can help me out with the following problem - Please imagine that I take a freely moving ball in 3-space and create a 'cage' around it by defining a set of impassible coordinates, Sc (i.e. points in 3-space that no part of the diffusing ball is allowed to overlap). These poi...
Imagine a photo, with the face of a building marked out. Its given that the face of the building is a rectangle, with 90 degree corners. However, because its a photo, perspective will be involved and the parallel edges of the face will converge on the horizon. With such a rectangle, how do you calculate the angle in 2D of the vectors ...
Hi, In one of mine applications I am dealing with graphics objects. I am using open source GPC library to clip/merge two shapes. To improve accuracy I am sampling (adding multiple points between two edges) existing shapes. But before displaying back the merged shape I need to remove all the points between two edges. But I am not ab...
I'm stuck on this: Have a square. Put n points into this square so the minimal distance (not necessary the average distance) is the highest possible. I'm looking for an algorithm which would be able to generate the coordinates of all points given the count of them. Example results for n=4;5;6: Please don't mention computing-power ba...
I'm trying to implement an algorithm from a graphics paper and part of the algorithm is rendering spheres of known radius to a buffer. They say that they render the spheres by computing the location and size in a vertex shader and then doing appropriate shading in a fragment shader. Any guesses as to how they actually did this? The po...