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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2answers
57 views

Gradient of an angle in terms of the vertices

Let $\theta(\vec p, \vec q, \vec r)$ be the angle theta between 3D real vectors $(\vec{q}-\vec{p})$ and $(\vec{r} - \vec{p})$. What is a simple expression of $\nabla \theta$ in terms of $\vec{p}$, ...
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0answers
11 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
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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 ...
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0answers
34 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
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0answers
17 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 ...
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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 ...
3
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4answers
230 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
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1answer
324 views

Calculating normals for a polygon mesh (3D computer graphics)

I want to write a program to generate arches, a common architectural form, and export them to a wavefront object format for sharing with various three dimensional graphics editors. To do this, I need ...
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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 ...
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0answers
25 views

3D vector perpendicular calculation

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 ...
0
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2answers
34 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 ...
3
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1answer
404 views

3D Rotation Decomposition?

I have a 3D local xyz coordinate system placed in a world ENU (East-North-Up) coordinate system. The current relationship ...
4
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2answers
56 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
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1answer
33 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
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1answer
364 views

Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining ...
6
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2answers
175 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 ...
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3answers
43 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
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1answer
629 views

How to find line parallel to direction vector and passing through a specific point?

I am give the point $(1,0,-3)$ and the vector $2i-4j+5k$ Find the equation of the line parallel to vector and passing through point $(1,0,-3)$ Could one use the fact that the dot product between the ...
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6answers
9k views

Find if three points in 3-dimensional space are collinear

Find if the points joining $A=(6,7,1), B=(2,-3,1)$ and $C=(4,-5,0)$ are collinear. How to determine collinearity in three dimensions? In two dimensions, one can compare the slopes of segments ...
0
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0answers
16 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
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1answer
25 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
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2answers
23 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 ...
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2answers
49 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 ...
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4answers
84 views

Best program for 3D plotting

I've hit a roadblock with pgfplots where it has difficulty plotting multiple functions at the same time in 3D. As it states in the manual on page 114, "it cannot combine different \addplot commands, ...
0
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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
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3answers
40 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
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1answer
330 views

How do you get 3D gradient direction and magnitude?

I know that we can get the magnitude and direction from 2D gradient ? 1) mag(Gx,Gy) = sqrt ( Gx^2 + Gy^2 ) 2) angle(Gx, Gy) = tan^-1 (Gy/Gx) What about in ...
2
votes
1answer
351 views

Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
0
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1answer
22 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 ...
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0answers
13 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 ...
2
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1answer
43 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 ...
0
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1answer
560 views

Equation of plane through intersection of planes and parallel to line

Find the equation of the plane through the intersection of the planes of $x-2y+z=1$ and $2x+y+z=8$ and parallel to the line: $\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{1} $ I'm facing difficulties ...
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2answers
58 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 ...
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1answer
46 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 ...
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0answers
52 views

Intersection between $2$ lines (3D). This doesn't have a solution does it?

so I was looking through an old exam and this question was given: The teachers answer was the point $(9, -9, 21)$ I tried solving this myself, I got $x = x$, $y = y$, but I could not find a point ...
0
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1answer
125 views

Rotate object around a fixed coordinate axis

I am trying to let the user of my app rotate a 3D object drawn in the center of the screen by dragging their finger on screen. A horizontal movement on screen means rotation around a fixed Y axis, and ...
0
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2answers
39 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 $(1, 2, 7)$.
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2answers
409 views

To find the center of gravity of a homogeneous tetrahedron

The center of gravity coordinates of a triangle can be calculated $O(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})$ where $P_1,P_2, P_3$ are the corner points of a homogeneous ...
10
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4answers
216 views

Tricky 3d geometry problem

We have a cube with edge length $L$, now rotate it around its major diagonal (a complete turn, that is to say, the angle is 360 degrees), which object are we gonna get? Astoundingly the answer is D. ...
0
votes
1answer
15 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
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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
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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
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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 ...
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0answers
47 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
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1answer
273 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? ...
0
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1answer
1k views

Finding the missing vertex $(x,y,z)$ of a rectangle whose other vertices are defined.

How do I find the missing fourth vertex $D$ of a rectangle, which has three vertices defined? The Equation of the plane being $ax+by+cz+d=0$ Where, $a = (By-Ay)(Cz-Az)-(Cy-Ay)(Bz-Az)$ $b = ...
1
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0answers
24 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
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1answer
26 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 ...
0
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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
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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 + ...