The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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1
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3answers
35 views

finding a third 3d point in a series

Given two three dimensional points. find the z coordinate of a third point that has two known coordinates. I'm not entirely sure how to solve this system. I'll be implementing this into an algorithm ...
0
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1answer
23 views

Is it possible to create a parabola by intersecting a hyperboloid of one sheet and a plane?

By which I mean, is there anyway that the intersetion of a plane and a hyperboloid of one sheet will be a parabola? I know that intersecting a plane and a cone so that the plane is parallel to the ...
4
votes
2answers
36 views

How to calculate line-line distance when cross product of directions is 0?

I have the lines $$\frac{x-1}{2} = 1-y = \frac{z-2}{3} \tag{1}$$ and $$\frac{x+1}{4} = \frac{4-y}{2} = \frac{z+1}{6} \tag{2}$$ I want to compute the distance between them. I started by putting ...
2
votes
0answers
22 views

Calculate vector of an object aligned to another object in a 3D envorionment

I have an object (100x100x5) with given coordinates and angles. Now I want to place another object aligned to the left/right side of the "original" object. On the X-Axis I need to substract/add 100, ...
-2
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1answer
14 views

Determine outer points given more than 2 points [on hold]

Given I have 5 points, how do I determine outer points?
1
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3answers
56 views

What does the 2nd degree derivative of a cubic Bezier curve actually represent?

I have a $3D$ Bezier curve. Each co-ordinate along its path is defined by the equation: $$ f(t) = t^3 \bigl(a_2+3(c_1-c_2)-a_1\bigr) + 3t^2 (a_1-2c_1+c_2) + 3t(c_1-a_1) + a_1 $$ where $a_1, a_2$ are ...
1
vote
0answers
15 views

How to compute the best fitting frustum for a set of points?

I am struggling with a problem that I am sure is well known, but I could not find any answer using google or searching on MathOverflow. I have a set of 3D points (x,y,z) and a camera reference frame ...
0
votes
1answer
16 views

what is the difference between an elliptical and circular paraboloid? (3D)

My textbook uses the terms interchangably, and they look the same in graphs, so I was wondering if there a difference between the two? Thanks!
1
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2answers
25 views

How to calculate the center of mass for a cloud of 3D spheres?

Given the spheres in 3D space: center(xi,yi,zi), radius and density and the info is stored in an array sphere_data[n][5]: // Sphere_ID x y z radius density 1 x1 y1 z1 rad1 ...
0
votes
0answers
26 views

Finding position of point (in 3D space ) which are at x,y offset from corner of a rectangle in 3D world

So I am writing a 3D graphic software. And I am stuck at mathematical problem. Mathematically speaking: There's a rectangle (plane) of finite size in 3D space. It can be of any orientation and ...
2
votes
1answer
64 views

How can we prove that a three legged chair will never be wobbly?

I am taking the geometry approach. We know from intuition that more than three legs on a chair will make it unstable if any of the legs have a different length than the others. So by "wobble" I mean ...
0
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0answers
15 views

Cone with 3 mutually perpendicular generators [closed]

what is general equation of cone touching coordinate planes and please show it diagrammatically
1
vote
1answer
26 views

Expression of rotation matrix from two vectors

What is the matrix expression of the rotation matrix in 3D which turns a vector $\vec{a}$ into a vector $\vec{b}$, with both vectors given by their coordinates? ($\vec{a} = (a_x, a_y, a_z)$ and ...
0
votes
1answer
27 views

Determining if a point is inside an infinite 3d elliptical tilted cone

I have an infinite 3d elliptical, tilted cone that is defined by a vertex point P(x,y,z) and by 4 angles: the first pair of angles represent the spatial orientation of the cone: θ is the polar angle ...
1
vote
2answers
123 views

Plane intersecting all the lines

This might sound a bit stupid or ill thought, but I am having trouble visualizing it and proving it. Given a finite set $L$ of straight lines in $\mathbb{R^3}$ is it always possible to find a plane ...
1
vote
0answers
12 views

Calculate the plane angle from 2D plane

I am analysing a squared plane from a perfect cube. This plane is distorted by the perspective view of a camera. I would like to know ask please, some approaches of how could I get to know the ...
0
votes
1answer
18 views

What does this volume represent?

I have been trying to draw this out for an hour now and cannot visualize it. $x$ is between $0$ and $1$, $y$ is between $0$ and $x$, and $z$ is between $x^{2}+y^{2}$. The $z$ line is just a ...
0
votes
0answers
40 views

How to draw regular tetrahedron from center?

How to calculate all four points of regular tetrahedron if you have x,y and z for center point and x, y and z axis rotation and size of tetrahedron? I want to write this in java script and this is ...
0
votes
0answers
19 views

How to construct a surface with a closed curve?

in 3-dimension, suppose that there is a smooth closed curve $C$. Can I say that there is a smooth simply connected(no holes) surface whose boundary is $C$? and is it unique?(I guess not) like ...
0
votes
1answer
17 views

Square surface with four fixed points

I'm looking for a function of two variables, $f(x, y)$, that satisfies the following constraints: $f(0, 0) = z_1$ $f(0, 1) = z_2$ $f(1, 0) = z_3$ $f(1, 1) = z_4$ and within the unit square, it ...
0
votes
0answers
8 views

Find the Area of 3d object? [duplicate]

I know I've asked a similar question, but I cannot get the answer. If some 3d object are $(1.2*10^4)$ times bigger than other 3d objects. What is the area of the 3d objects, in square meters, if the ...
0
votes
2answers
42 views

The point A (4, 3, c) is equidistant from the planes P1 and P2. Calculate the two possible values of c

The point $A (4, 3, c)$ is equidistant from the planes $P_1$ and $P_2$. Calculate the two possible values of $c$. Plane $P_1$ has equation $r\cdot (2,-2,1)=1$ Plane $P_2$ has equation $r\cdot ...
-1
votes
0answers
26 views

3D vector perpendicular calculation [on hold]

Three points $A(6,7,-6)$,$ B(0,0,0)$ and $C(2,6,9)$ are given which are the vertices of a cubes. Find the coordinates of another vertex not on the $ABCD$ plane. I found the answer by finding the ...
4
votes
2answers
64 views

How do I find the Intersection of two 3D triangles?

I've got a rather complicated geometry problem that I'm trying to solve - how to find the intersection between two triangles in 3D space. I've looked around at other questions and answers on this site ...
0
votes
1answer
34 views

Three-Dimensional Metrics as Deformations of a Constant Curvature Metric?

I read the following paper Three-Dimensional Metrics as Deformations of a Constant Curvature Metric and discovered the following result: I have three questions: (1) Is $h$ also a conformally flat ...
1
vote
3answers
44 views

Geometry - Determine all points along a ray from starting coordinates and direction

I am working on a video game. I need to determine each point along a ray with every x interval with the following information: X, Y, Z coordinates of the starting point of the ray, and, X, Y, Z ...
0
votes
0answers
17 views

Reflect vector across plane with offset.

I need to mirror an object across a plane in a 3D application. I've been able to do so, however it does not factor in the position of the plane, it only assumes that the plane is at the origin. Here ...
0
votes
1answer
27 views

Calculating plane rotation angles

Let's presume I have an arbitrary plane, for sake of simplification, centered at (0,0,0), described by coordinates of 4 vertices (and normal if needed). Is there any way to describe this plane as ...
2
votes
2answers
24 views

possible polyhedra from euler's formula

I'm not very clear with the euler's formula, and I couldn't find it anywhere. I'm sorry if it is a double post. F + V - E = 2 Is the euler's formula. If the equation balances, is it polyhedra all ...
0
votes
2answers
52 views

Convert a 2D point to 3D on a plane

I have a 2D point and a 3D infinite plane(defined by a 3D point and its normal), I want to convert 2D point to 3D point by projected 2D point onto 3D plane surface. I'm weak in math, I need a method ...
0
votes
0answers
26 views

Can a line in 3-space have all direction cosines $=\frac{1}{2}$

I immediately found that it is impossible since the squares of the direction cosines have to add to 1 and $3 \times (\frac{1}{2})^2 \neq 1$. However, the textbook asks to "interpret geometrically", ...
4
votes
3answers
41 views

Three dimensional rotation of equations.

I have a set of equations that describe a wire in (100) direction. I want to rotate the wire such that it's in the direction (111). My initial plan (which failed) was to use Euler coordinates and ...
0
votes
1answer
24 views

What function can produce a perfect saddleback plot and fulfil the following requirement?

I need to find a function that produce a good saddleback plot. The function has the following requirements: Having 2 arguments: x and y Both x and y are natural numbers The result of the function ...
1
vote
0answers
16 views

How do I calculate 3D movement based on yaw, pitch and roll?

I'm creating a 3D game demo and I need to calculate the position of the player in the space (i.e. the player's x, y and z coordinates). I understand that this would be affected based on the camera ...
6
votes
2answers
178 views

Mystical looking graphs (three-dimensional rotating hearts)

Plop the following into Google: $$ 2-\sqrt{1-x^2-(y-|x|)^2}\cos(30(2-x^2-(y-|x|)^2)),\tag{1}\\ \text{$x$ is from $-1$ to $1$, $y$ is from $-1$ to $1.5$, $z$ is from $1$ to $2$} $$ Here is the result ...
2
votes
1answer
45 views

Normal of a coons patch at a given point

Disclamer: Rendering the Coons patch is part of 3D Graphics homework, but finding the normals at a given point isn't. Just curious. Here's what I got so far: It's a Coons patch defined by four ...
-1
votes
1answer
47 views

3-Dimentional array

I'm good in 2-D array which is the regular array that has rows and columns, but I have to deal with the 3D array and I can't imagine it, I tried searching for it but with no clue. Any big example of ...
0
votes
2answers
40 views

How to find the vector equation of a plane given the scalar equation? [closed]

How would I find the vector equation of the plane: $x + 2y + 7z - 3 = 0$ So far, I found the normal vector: it's $(1, 2, 7)$.
0
votes
1answer
16 views

Extending (projecting) a line in $3D$ space

So I have two points in 3D space, lets call them $p_1=(2,1,-1)$ and $p_2=(3,2,-2)\ $. This is all the information I have about these points. If I wish to extend this line to a $p_3$, how would I do ...
0
votes
1answer
31 views

Perpendicular Lines.

If two lines $L_1$ and $L_2$ in space, are defined by: $$L_1=\{x=\sqrt{\lambda}y+(\sqrt{\lambda}-1)\\z=(\sqrt{\lambda}-1)y+\sqrt{\lambda}\}\text{ and ...
-2
votes
2answers
59 views

Volume and surface area of a drilled out cube (BM01 2010/11 Contest Question 2)

Let $s$ be an integer greater than $6$. A solid cube of side $s$ has a square hole of side $x < 6$ drilled directly through from one face to the opposite face (so the drill removes a cuboid). The ...
0
votes
0answers
30 views

Rotational matrices

I apologize ahead of time that math isn't my strong suit, I understand most the basic concepts but lots of gaps. So forgive me if i miss use a concept. So I am working in a 3d engine integrating a ...
2
votes
4answers
59 views

Algorithm to generate a hill

Setup I recently started to work with Unity. I want to generate a custom terrain at runtime. To do this i take a grid with a variable amount of squares. For each of the squares i calculate the height ...
0
votes
0answers
48 views

Find the UV distance from a point on a plane with any normal

I have a plane defined by a point(p1) on the plane and its normal (n). I have calculated the point of intersection for another point (p2) by http://geomalgorithms.com/a04-_planes.html. These two ...
0
votes
1answer
279 views

How do you find the cross sectional area of a Tetrahedron?

How is vector's related to this question? If so, how can you use the vectors? I understand that its a triangular pyramid. But how can you show the cross sectional area for any generalised height? ...
1
vote
0answers
27 views

Mapping A point from one 3D Coordinate System to Another 3D coordinate System with Euler Angles between the two systems given

Suppose I have a point in the green coordinate system, and I wish to describe it in reference to the orange coordinate system. I know the roll, pitch, and yaw of the green system with respect to the ...
0
votes
1answer
34 views

Equation of plane parallel to a vector and containing two given points

I'm not sure how to solve this. I started by finding the equation of the line AB.
1
vote
2answers
48 views

How to get projection of ellipsoid onto sphere

I'm trying to get the projection of an ellipsoid onto a sphere. Depicted in the image below, I need the projection of the red ellipsoid onto the unit sphere at the origin. I have tried various ...
1
vote
1answer
39 views

How can I move a point along a line in 3D space to reach a target dot product with a fixed reference point?

Suppose a point in 3D space, Q. For any other point x in that space, Let Q(x) be the unit vector pointing from x towards Q. I also have a line L in 3D space, and a point on this line P. L = {P + ...
0
votes
1answer
27 views

coordinates of 3rd point (vertex) of a right triangle knowing lengths and direction

In a last post I wanted to know the 3rd point of vertex, actually I have some similar problem .... I think I have all data.. for example...: 3 vertex cordinates in order to have the direction(gray ...