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Questions tagged [geometry]

A branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

31
votes
2answers
9k views

I'm rotating an object on two axes, so why does it keep twisting around the third axis?

I see questions come up quite often that have this underlying issue, but they're all caught up in the particulars of a given feature or tool. Here's an attempt to create a canonical answer we can ...
18
votes
2answers
21k views

How can I convert a mouse click to a ray?

I have a perspective projection. When the user clicks on the screen, I want to compute the ray between the near and far planes that projects from the mouse point, so I can do some ray intersection ...
39
votes
6answers
5k views

Hexagon collision detection for fast moving objects?

A object has a position and a speed vector. Usually only the position is used to check if two objects collide, this is problematic for very fast moving objects as it can happen that the object moves ...
5
votes
1answer
4k views

Generating spherical world from heightmapped terrain

I am using a standard heightmapped procedural terrain in my project. However, I want the terrain to appear spherical when the user zooms out. This is an attempt to simulate the appearance of a ...
11
votes
1answer
1k views

Algorithm for “healing” multiple rectangles into a smaller number of rectangles?

Say I have a grid of rectangles of different shapes and colors and I want to reduce (reasonably close to optimal is fine, optimal is not necessary) the number of rectangles to represent the same ...
9
votes
3answers
6k views

2D isometric: screen to tile coordinates

I'm writing an isometric 2D game and I'm having difficulty figuring precisely on which tile the cursor is. Here's a drawing: where xs and ys are screen coordinates (pixels), xt and yt are tile ...
12
votes
2answers
5k views

Arbitrary Rotation about a Sphere

I'm coding a mechanic which allows a user to move around the surface of a sphere. The position on the sphere is currently stored as theta and ...
8
votes
2answers
3k views

How does Unity3D lower an imported .obj vertex count?

I have a question regarding how Unity3D handles importing of .obj files. I'm importing this teapot: http://groups.csail.mit.edu/graphics/classes/6.837/F03/models/teapot.obj The number of vertices ...
5
votes
1answer
7k views

How do I find rotation in 3D based on a vector/normal?

I've been playing with Blender and Python, doing basic things like accessing vertices/normals,etc. I can get the normal of each face of a mesh. I was wondering, how can I get the rotation of a face ...
24
votes
3answers
31k views

How do you programmatically generate a sphere?

Could someone please explain how it would be possible to create a sphere vertices, indices and texture coordinates? There is a surprising lack of documentation on how to do so and it is something that ...
31
votes
1answer
8k views

How do you turn a cube into a sphere?

I'm trying to make a quad sphere based on an article, which shows results like this: I can generate a cube correctly: But when I convert all the points according to this formula (from the page ...
12
votes
1answer
2k views

How do I make a curved surface out of rectangular blocks?

For a Peggle-like game, I want to make blocks that follow a curve, like this: The blocks would then disappear as the ball hits them. I managed to draw some horizontally, but I'm having trouble ...
27
votes
6answers
15k views

How do I calculate distance between a point and an axis-aligned rectangle?

I have a 2D rectangle with x, y position, height and width, and a randomly positioned point nearby. Is there a way to check if this point might collide with the rectangle if it is closer than a ...
10
votes
1answer
7k views

Circle-Line Collision Detection Problem

I am currently developing a breakout clone and I have hit a roadblock in getting collision detection between a ball (circle) and a brick (convex polygon) working correctly. I am using a Circle-Line ...
5
votes
1answer
6k views

Sphere-Sphere intersection and Circle-Sphere intersection

I have code for circle-circle intersection. But I need to expand it to 3-D. How do I calculate: Radius and center of the intersection circle of two spheres Points of the intersection of a sphere and ...
5
votes
1answer
773 views

rotating an object from sourceAngle to destAngle, both 0-359, clockwise or counter clockwise?

I've got a game object i need to rotate. It's current angle is player.rotation, the destination is targetAngle, both in degress, 0 to 359. I've got a function named rotateDirection(float sourceAngle, ...
10
votes
3answers
4k views

How do I translate a spherical coordinate to a Cartesian one?

Could someone point me in the right direction as to how this might be achieved? 3D math / geometry often throws me. I'm looking for something like this (ideally in C#): ...
7
votes
1answer
2k views

Converting between Spiral Honeycomb Mosaic and axial hex coordinates

There seems to be quite a lot of logic in dealing with hexagonal grids using a system of axial coordinates like the one described here. In doing some reading about hex grids, though, I ran across the ...
11
votes
2answers
2k views

How to limit click'n'drag movement to an area?

I apologize for the somewhat generic title. I'm really don't have much clue about how to accomplish what I'm trying to do, which is making it harder even to research a possible solution. I'm trying ...
5
votes
1answer
3k views

Morph a sphere to a cube and a cube to a sphere with GLSL

I'm getting started with GLSL with quartz composer. I have a patch with a particle system in which each particle is mapped into a sphere with a blend value. With ...
4
votes
2answers
2k views

Generate Geodesic Sphere from Hex and Pentagons

I have two polygonal meshes, a hexagon and a pentagon (They are tiles in a strategy game). I want to use them to construct a geodesic sphere (https://upload.wikimedia.org/wikipedia/commons/e/e7/G%C3%...
1
vote
4answers
8k views

How does atan2 work when getting angle of a vector?

I know that atan2 gives me the absolute angle of any vector. But it doesn't give a value from 0 to ...
4
votes
2answers
5k views

Triangle-Plane intersection in 3D space

I would like to clip a triangle if its bounds lie partially out of a cube. I guess I would need some kind of Triangle Plane intersection code - I'm not well versed with math but I do have the points ...
2
votes
1answer
2k views

How do I determine the collision normal in an axis aligned bounding box collision?

I have a 3d moving box and a stationary box. I can detect collisions ok but now I would like to slide the moving box against the stationary box as a collision response. For this I need the normal of ...
1
vote
2answers
12k views

How to determine the point of intersection of two lines? [closed]

I have two lines say P1( 0, -1, 0, -1 ) and P2( -1, 0, 0, -1 ). Since I'm working in 2D, there is no Z component. The x,y,z components are normals and the w component is the distance from origin. I am ...
14
votes
2answers
23k views

How do I use the dot product to get an angle between two vectors?

I am learning to use normalized vectors in my games. I've learned that in order to know the angle between two vectors, I can use the dot product. This gives me a value between -1 and 1, where 1 ...
19
votes
5answers
2k views

How can I tell whether an object is moving CW or CCW around a connected path?

Lets say we have a jagged shape: And two creatures moving along it's outline. Then we smooth the shape completely by pulling the corners out. We get this: It is easy to see now that Orange is ...
8
votes
3answers
9k views

Decomposing a concave mesh into a set of convex meshes

I'd like to be able to decompose a concave mesh into a set of convex meshes for 2 reasons: Transparent rendering Physics shapes Is there an algorithm that takes a set of triangles (concave) as input ...
9
votes
2answers
3k views

Geometry System of Populous: The Beginning [closed]

I want to to develop a game like Populous: The Beginning with my friend. But we could not find out what type of geometry they have used for the world. We know that - all tiles have the same size - ...
25
votes
4answers
7k views

Is the Manhattan distance monotonic when used as heuristic function?

I have a square-based map. Only horizontal and vertical movement is allowed (no diagonals). Movement cost is always 1. I'm implementing an A* algorithm on that map, using the Manhattan distance as a ...
14
votes
4answers
1k views

Algorithm for creating adjacent triangles

I have a system where you can click once to place a node in a scene. When you place 3 nodes, it forms a triangle. When you place any future nodes, it creates a new triangle by joining that node to the ...
5
votes
2answers
937 views

a flexible data structure for geometries

What data structure would you use to represent meshes that are to be altered (e.g. adding or removing new faces, vertices and edges), and that have to be "studied" in different ways (e.g. finding all ...
11
votes
4answers
424 views

How do I interpolate around a rectangle?

I want to make a fancy animation where a point travels around a rectangle. I want to find the point's position at a time t. The rectangle is given by ...
8
votes
1answer
23k views

How to calculate a 3x3 rotation matrix from 2 direction vectors?

I've got 2 direction vectors, for the X axis and the Y axis of the object. How do I calculate the rotation matrix of the object using these?
8
votes
4answers
4k views

How do I efficiently check if a point is inside a rotated rectangle?

Part for the sake of optimization, part for learning purposes, I will dare to ask: How can I most efficiently check whether a 2D point P is inside a 2D rotated ...
5
votes
1answer
9k views

How do I find the circumcenter of a triangle in 3D?

I want to find the circumcenter of a triangle. Wolfram only shows how to find the circumcircle of a triangle in R2. How can I find the circumcenter of a triangle in R3?
6
votes
2answers
840 views

Robust line of sight test on the inside of a polygon with tolerance

Foreword This is a followup to this question and the main problem I'm trying to solve. My current solution is an hack which involves inflating the polygon, and doing most calculations on the inflated ...
6
votes
2answers
269 views

How do you calculate if a line is facing a curve?

Given the 2 points describing a line segment, and the 3 points describing a quadratic bezier curve, how do you calculate if the line is facing towards or away from the curve? The line has a fixed ...
2
votes
1answer
1k views

How do I calculate the distance between a point and a rotated rectangle?

This question is similar to another one about axis-aligned rectangles. However, I specifically want to calculate this for rotated rectangles. I have a rectangle with a (cx, cy) for the center point ...
6
votes
2answers
882 views

Perspective in early pseudo-3d games

Please take a look at the screenshot below, from the old classic Space Harrier. My question regards the curved perspective on the chequerboard 'ground'. It's got a strangely curved geometry (I ...
6
votes
4answers
4k views

How do I restrict the movement of a point to within a radius of another?

I have a situation where a sprite's center point needs to be constrained within a certain boundary in 2D space. The boundary is circular, so the sprite is constrained within a radius. This radius is ...
5
votes
2answers
1k views

Generating geometry when using VBO

Currently I am working on a project in which I generate geometry based on the players movement. A glorified very long trail, composed of quads. I am doing this by storing a STD::Vector, and removing ...
4
votes
2answers
1k views

Repairing back-facing triangles without user input

My 3D application works with user-imported 3D models. Frequently, those models have a few vertices facing into the wrong direction. (For example, there is a 3D roof and a few triangles of that roof ...
3
votes
2answers
983 views

Most efficient way to get the world position of the 8 vertexes of a Box Collider (C#)

What I am looking for is the most efficient way to get the world position of the 8 vertexes of the Box Collider of a freely rotated Gameobject. I cannot use collider.bounds since object is rotated, ...
2
votes
1answer
944 views

How do I make a low pass filter (average of readings over time) for compass?

I'm making a prototype for android that pulls compass data from the phone. I want to stabilize it so it is less jerky, by taking the average of the last couple of readings. I have done this for ...
0
votes
1answer
788 views

How to modify normal vectors with a tranformation matrix

Transformation is quite simple when it comes to Position or Color of the vertex, for Position just multiply matrix * vector and for color just don't do anything, but my question now is: How to handle ...
5
votes
1answer
185 views

trapped inside a Graph : Find paths along edges that do not cross any edges

This is a graph based platformer level and the round shapes are creatures. I am looking for a path traveling along edges that does not cross other edges(To simulate the creature crawling on the ...
5
votes
3answers
926 views

Adding tolerance to a point in polygon test

I've been using this method which was taken from Game Coding Complete to detect whether a point is inside of a polygon. It works in almost every case, but is failing on a few edge cases, and I can't ...
4
votes
3answers
10k views

How to move an object along a vector

Let's say I got an object A and object B in a 2D game. I create a vector leading from A to <...
4
votes
1answer
854 views

Explain this line segment intersection code

I've been reading this article on pathfinding over polygon meshes using line-of-sight, and in the article are several code snippets. One of them, the one I'm trying to understand, is a simple function ...