Questions tagged [mathematics]

Mathematics questions deal with the arithmetic, geometry, calculus, formulae and other calculations used in the development of a game.

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0
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2answers
98 views

Rotating quaternion smoothly with acceleration and deceleration

I have this code for my linear acceleration and deceleration. ...
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1answer
64 views

How to do topdown collisions properly?

I'm trying to achieve grid/tile based collisions like "a link to the past"; here is an article showing it off (sliding off the corners and such). I'm currently using this type of collision ...
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1answer
31 views

Move vector A to vector B but stop X distance before reaching vector B and always be in front

I believe this is basic vector math, but I'm struggling with it. I have 2 objects (3D space, x, y, z), A (weapon) and B (camera). I want to move A to B's location, but then offset A from B so that it ...
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1answer
79 views

Problem with InverseTransformDirection and non-uniform scale

I made the plane to work with mesh vertices ...
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1answer
83 views

finding the angle of rotation of a 3d line

I have a line segment joining two 3D points AB, and a vector V which is normal to it. I need to know the angle of AB in the plane described with V as the plane normal, that is: in the plane of the two ...
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1answer
45 views

How to get all tiles along a straight vector path?

Let's say I have a 100x100 map of tiles where each tile is 16x16 pixels. How would I get all tiles along a path? For example, let's say I wanted to get a list of all tiles along the shortest direct ...
2
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1answer
123 views

Determining the price of a trade good depending on supply and demand of a marketplace

I've been meaning to add a market/trading system in my space-themed game where a player can buy from one station and sell it to another for profit, etc. (Examples would be Starsector, Elite: Dangerous,...
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2answers
103 views

Transactions on lists of coins of different values

For learning purposes, I am developing the first steps of an idle game with exponentially higher income numbers. Usual int, long, etc. can't store big enough numbers for that. I looked through many ...
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1answer
41 views

Angle between start and current rotation

I'm facing problem of the operations on rotations. I have a wheel with a start rotation of (0, 0, 0). The player has to rotate wheel 270 degrees in Y axis either left or right. During the rotation ...
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1answer
72 views

Offscreen waypoint indicator using X and Y screen position

I was wondering how I could achieve an offscreen indicator effect that helps direct the player to the next waypoint. My game is 3D, most solutions I have found are for 2D games (i.e Asteroids). See ...
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0answers
92 views

How to implement PCSS properly?

I'm trying to implement PCSS in OpenGL/GLSL, but I have problems understanding the details especially the conversions between the coordinate spaces. The existing implementations are so different from ...
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0answers
38 views

What is the math to project a 3D object's center onto a 2D plane?

What I really need is the x,y of the object when it is outside of the screen: I'm actually coding a UI in Objective-C, not a game. In this different kind of UI you navigate a 3D space with objects. ...
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1answer
38 views

How to interpolate colors around the spectrum of hues?

I wanted to generate a 7 segment display whose color brightness varies with time, this can be done by just using linear relationship. ...
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1answer
641 views

How does glm::lookAt produce a View Matrix?

Say we do this: glm::mat4 View = glm::lookAt(glm::vec3(4,3,-3), glm::vec3(0,0,0),glm::vec3(0,1,0)); And after printing to the console with glm tostring (column ...
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0answers
22 views

Efficient way to compare vectorial direction?

I have a bunch of random vectors representing a direction and four other vectors that we can distinguish with their pyramidal arrows at their extremity, they represent a boundary what i'd like to do ...
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1answer
53 views

Why my calculated value is far different from actual value?

I using CharacterController and not using a Rigidbody so I writing a script for downward velocity which is velocity=-9.81*(time) ...
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1answer
76 views

Is an inertia tensor in local-space always diagonal?

I'm looking at the implementation of a physics engine and I observe that the inertia tensor of a rigid body, in local-space coordinates, is stored as a 3 dimensional vector, rather than a 3x3 matrix, ...
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0answers
56 views

Slope detection in 2D platformers

I am currently shifting from unity to monogame to make 2d platformers. I am not aware of any sort of "raycasting" provided with monogame, I am aware of AABB collision detection and I am ...
2
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2answers
172 views

How to smoothly interpolate 2D camera with pan and zoom

I'm developing an animation application with a 2D virtual camera. The camera viewport can be positioned and scaled in the keyframes and is then interpolated to render the final animation from the ...
8
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2answers
2k views

How to create a spiral brightness gradient

I am stuck on creating a brightness gradient that looks as below(the values are continuous from the inner circle). What formulae can create such brightness gradient? So that when _Time is added to it, ...
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2answers
97 views

Is there a simpler way to simplify the if statement? [closed]

The code below generate angle and radius based brightness gradient. As you can see I need to use 3 if statement to define 3 circle, wonder is there a single code that can create nth circle ...
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1answer
152 views

Help understanding radar sweep effect in shader code

Several days ago I asked about this question: How to construct a propeller clock in Unity? But I don't understand how the answer works. I have 0 knowledge about shaders, so I picked up a tutorial to ...
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1answer
93 views

Cylindrical billboarding around an arbitrary axis in geometry shader

I found an answer on this site relating to this question already, but it doesn't seem applicable in the context of my project. Basically I'd like to create a method which fits this signature: ...
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0answers
164 views

Create Mesh in gap between tiles (in Unity3D)

I am loading two kinds of tiles (meshes in tile format) in Unity, both are placed in the environment correctly but there is a gap between these two tiles (see the picture below). I want to fill this ...
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0answers
37 views

How to fill with empty space with retangles

I have a 'square' class with the representation of its limits from the variables x1, y1 and x2, y1 these variables define points 1 and 3 of the same, in this case the coordinates would be (0,0), (10, -...
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1answer
46 views

How to create a Decisecond(0.1second) function that can use in the code?

I create a circular object and pivot the minute and second pointer on the middle of the object as below. Below is the code I use. ...
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1answer
59 views

Object to reach height depending on its gravity and mass

A mathematician will probably think this was a silly question, but I'm not one and I'm in need of help :D I'm working in Godot and with its RigidBody2Ds (objects ...
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2answers
291 views

How to project a 3D circle/ellipse to 2D?

The 3D ellipse is represented by its center and the vectors for its major and minor axes and the 2D ellipse by its center, the length of the major and minor axes and the angle between the major axis ...
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2answers
65 views

What rotation needs to be applied to align mesh with expected axis of target?

I'm using LWJGL and JOML to create a 3D view of hexagons whose positions lie on a torus. I have a number (NxM) hexagons, whose centres and normals I have calculated to be placed on the torus to ...
0
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0answers
86 views

In a shader how to map UV coordinates of texture to the UV coordinates of a tile in a tile set?

I am writing a fragment shader for a tile set. In the shader I have the UV coordinates of the whole texture, however, I am interested in the UV coordinates of the current tile that is being rendered. ...
0
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1answer
137 views

How do you detect which side of a cube is facing up/down/left/right?

Please imagine a scene that shows a cube. Both the camera and the cube can be randomly positioned and rotated. How can you tell which side of the cube is facing up/down or left/right? Or in other ...
2
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1answer
703 views

World position into local position

I want to understand how I can convert world position of an object into local position. Especially how to deal with a rotation of objects. I'm testing transform.InverseTransform(...) methods. When ...
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0answers
18 views

Determining IF & WHERE a line intersects with a 2D plane (in 3D space) [duplicate]

The following problem I'm working on is for one of my favorite past-times: game development. Problem: We're in 3D space. I'm trying to determine if a line between two vectors in said space is passing ...
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1answer
102 views

Math question: How to move/extrude a cube's face in Unity?

The short question is: What's the math to move the face of a cube? I.e. how to stretch (or shrink) a cube in the direction of one of its faces? Here's a picture: The camera shows a cube (left). When ...
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0answers
103 views

c++/openGL 3D Bouncing Cube

I'm trying to write a little program with a bouncing cube but I can't find the right values for it. I have these lines: ...
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0answers
25 views

Statemachine to behaviour tree?

Background I was able to convert simple statemachines like this... Into a BT looking like this (Notation describtion)... ...
0
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1answer
155 views

How do I determine the player's grid position?

My original method for doing this involved taking the player's position, dividing it by the grid cell size, and rounding the result. This works for most cases except when I move my player up above y-...
0
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1answer
337 views

Verlet rope between two moving points connected with a spring joint?

I'm connecting two moving rigidbodies using a spring joint in Unity. Between them, a rope will be rendered using a line renderer and I want it to move realistically as the joints move, without physics....
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0answers
59 views

Frustum culling issue at oblique angles

I am using the following algorithm to test if my camera frustum contains an axis-aligned bounding box: ...
0
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1answer
93 views

Rotate relative to set point in a specified direction in a 3D space

I know there's a geometry formula to calculate the next point in rotation relative to another point in 2D but I'm working in 3D and I want to calculate the next position in specified direction as well....
1
vote
1answer
1k views

How to decompose a 4x4 TRS transformation matrix with negative scale?

As the title says I need to decompose 4x4 TRS transformation matrices and extract the proper scale vectors and the proper rotation vectors (or rotation quaternions). I know how to extract those ...
0
votes
1answer
215 views

Rotate object relative to camera position

I am trying to write code that is able to rotate object, based on camera position. So far I ended up with a code posted below. Moving mouse up and down (y input) caused to rotate object in y axis, ...
0
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1answer
51 views

How to tell which face of a cube is most visible to the camera?

Imagine a camera that shows a randomly rotated cube at an arbitrary position: The cube's pivot is in the center of the cube. This way its six faces could be referred as positive/negative X, Y or Z. ...
1
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2answers
167 views

How do I calculate/weight a diminishing damage formula based on N targets?

I'm making a game and had a look at the questions about calculating damage/diminishing returns here and here but I haven't quite been able to come up with a logarithmic function that satisfies this ...
1
vote
1answer
87 views

Calculating probabilities for a custom drop table system

I have a "drop table" / "loot table" / "item table" / "whatever you want to call it" system and I need to solve two Problems. Apologies in advance for the text ...
0
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1answer
77 views

How to Generate Level Map Based on Golden Ratio

I am trying to generate a map based on the Golden Ratio: a+b is to a as a is to b. I was looking at a JavaScript math library that had a built-in phi, but I wasn'...
1
vote
1answer
39 views

Can I get world-space z-near-plane vertices from projection matrix + z-near distance?

I'm trying to port ShaderToy VR shaders to WebXR (the new browser API for AR/VR devices). ShaderToy VR shaders expect two extra parameters: ray origin (view translation) and ray direction (unit vector ...
0
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0answers
66 views

Aircraft trajectory prediction

I have an aircraft that is controlled by player and i need to predict it's position at needed time. It's not a problem if the plane is just moving straight but most of the time aircraft is maneuring. ...
0
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2answers
211 views

When are oblique triangles used in game development?

I'm working on a project that explains how trigonometry is used in video games, and I need to mention oblique triangles. However, as far as I know, only right triangle diagrams are used in video games ...
6
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3answers
2k views

Rotation grid positions

I'm dealing with objects on 15x15 chunks in my game. I'd like the chunks to rotate, for example, rotation version 0 is the original position of 2,5; (EDIT: Oops, rotation 2 and 3 names need switching ...

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