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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3
votes
3answers
66 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
0
votes
0answers
25 views

How can we split a single rotation into two along orthogonal axes?

I have the following axis system, where the X-Y plane is horizontal and Z points 'up': I have a horizontal plane that I want to rotate so that the angle between it and the XY plane is theta. I ...
0
votes
2answers
57 views

Determining the equation of this 3D object

Does anyone know how I can determine the equation of the 3D object below? (Maybe there's a program that can do it?) I am looking for a formula to define this 3D object, but am having trouble finding ...
0
votes
0answers
91 views

Can 2 parallel lines be discriminated as 'away', 'beside' with respect to 3rd parallel line? [on hold]

I have nearly parallel several $3D$ line segments. Some line segments are located (blue line) beside to a specific line segment (black line) and some others (red line) located away from that line ...
2
votes
1answer
60 views

Creating an ellipsoidal 3D surface

I am trying to find the equation of a 3D ellipsoidal surface. I have thought of two approaches which are schematically shown below: By revolving an elliptical arc over a 3D elliptical path: Or by ...
1
vote
1answer
25 views

Construct a procedure which determines the location of the shadow of a rectangluar box.

I drew a 3d rectangular box on a coordinate plan consisting of x, y, and z. A procedure is to be created that will determine the location of the shadow of the box on one of the coordinate planes. I ...
0
votes
0answers
21 views

Non-standard 3D rotation of a set of points

I want to create a 3D surface as shown in the figure below. Toward this, I thought if I rotate a set of points in $xy$-plane on a elliptical arc I may be able to get such a surface. I was thinking of ...
1
vote
1answer
37 views

Calculate the viewing-angle on a square (3d-calc)

I'm in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 ...
0
votes
1answer
25 views

Determine similarity between two sequence of quaternions while allowing a degree of freedom around Z axis

A person holds his phone and rotates it in space in a sequence. I am able to obtain a sequence of quaternions from the phone's motion sensors representing the rotation of the phone from the phone ...
1
vote
5answers
301 views

Relation between edgelengths in a tetrahedron with two right angles and three equal edges

I have got a problem I can't solve myself. I had an attempt, but it's wrong. I was told to draw a grid of this tetrahedron and then it's easier to find a solution (I tried it, but I don't see ...
1
vote
0answers
30 views

Determine Euler Angles from look, up, and cross vectors

I have a spaceship flying through a $3D$ space. The flight is determined by applying a quaternion to the look, up, and cross vectors with the following scheme (this is working perfectly): starting ...
3
votes
2answers
1k views

Form a Parallelogram by 4 Points

This is a question from my school. The following is the whole question. The vertices of a triangle $A$, $B$ and $C$ are given by the points $(-1, 0, 2)$, $(0, 1, 0)$, $(1, -1, 0)$ respectively. ...
1
vote
4answers
5k views

Calculate distance in 3D space

Imagine I want to determine the distance between points 0,0,0 and 1,2,3. How is this calculated?
1
vote
1answer
320 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 ...
3
votes
1answer
268 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 ...
2
votes
3answers
1k views

How to show two points in $\mathbb{R}^3$ form a plane and determine equation?

Given two arbitrary equidistant points in $\mathbb{R}^3$, ($p$ and $q$), how would one show that they form a plane and what would the equation of that plane be? Defining two vectors in ...
0
votes
1answer
26 views

Volume of a cylinder cut by a plane

I've looked online but I can't seem to find a calculus proof for the volume of a cylinder cut by a plane. The question is:...
5
votes
3answers
21k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
0
votes
0answers
32 views

Slope of image side for 3D rotation

I had a new idea for an experimental 3D assembler (not a rasterizer). The idea requires that I get the slope of the top, bottom, left, or right depending on the $z_n$ axis. My idea works on two ...
1
vote
0answers
25 views

Find 3D concave hull based on original model and convex hull

I want to find the concave hull of a 3d model, with a threshold for the maximum edge size. Googling around let me to the following approach (mainly abstracting from 2d approaches): Determine the ...
-1
votes
1answer
33 views

Line of greatest slope

Assuming the plane $4x-3y+7z=0$ to be horizontal, find the equation of the line of greatest slope through the point $(2,1,1)$ in the plane $2x+y-5z=0$
1
vote
1answer
169 views

Getting a 3d linear equation knowing the rotation of an object

I have an object, a simple rectangle I rotate it by a certain degree using Euler Angles, in this case around Z, to make it easy lets say it's 45 degrees. Right now I want the yellow: Y-Axis linear ...
0
votes
1answer
355 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 ...
0
votes
1answer
18 views

Intersection point in a 3D figure

I was considering the maximum number of points in a 3D-figure such that all the internal line segments of the figure (all the lines that have endpoints as vertices of the figure, and go through the ...
0
votes
0answers
25 views

How to create cube in 3d with given center , height vector , width vector and depht vector?

I want to create cube in 3d. I have center point of cube, height vector , width vector and depth vector. using this information i want to create vector. e.g. Center point = (1, 5, 7) Height Vector = ...
0
votes
0answers
11 views

Smooth decrease in size when using the dimensions of a cube

I wrote a maze like script a while back, and added in a part which would decrease the size in a linear fashion, based on the percentage of completion. The idea was it'd provide a smooth transition ...
0
votes
0answers
14 views

Specific function

I'm looking for a functions with 2 parameters (to plot in 3D) which will satisfy the following criteria: ...
-1
votes
0answers
13 views

Are the diagonals of cube subset of it?

The intersection of a cube and one of its diagonals is what? 1) This diagonal 2) two of its vertices
0
votes
1answer
619 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
0
votes
1answer
35 views

When doing 3D rotations my angle flips 180 degrees

I'm implementing 3D rotations for a set of 3D circles. To do that I'm using the parametric equation as described in http://demonstrations.wolfram.com/ParametricEquationOfACircleIn3D/. It works as ...
1
vote
1answer
83 views

Incorrect angle detected between two planes

I want to calculate the angle between 2 planes, Reference plane and Plane1. When I feed the X,Y,Z co-ordinates of pointCloud to the function plane_fit.m (by Kevin Mattheus Moerman), I get the output ...
12
votes
1answer
200 views

Every three of $n$ points is the vertices of an isosceles triangle. What is the max of $n$?

Suppose that we have $n\ (\ge 3)$ points in the three dimensional space and that every three of the $n$ points is the vertices of an isosceles triangle. Here, suppose that the vertices of an isosceles ...
0
votes
0answers
23 views

Change of co-ordinate frame

Hi Can someone help me with this question. Say point P and u, v, w are three orthogonal-normalized vectors whose co-ordinate are: P = [Xp, Yp, Zp], u = [Xu, Yu, Zu], v = [Xv, Yv, Zv] and w = [Xw, Yw, ...
1
vote
2answers
27 views

How to interpret the equation of a line in 3D through two points, when there are $0$s in the denominator? [closed]

If $A=(0,0,0)$ and $B=(1,0,0)$ are two points of a line in three dimensions, I think its equation should be $$\frac{x-0}{1}=\frac{y-0}{0}=\frac{z-0}{0}\tag1$$ according to the formula ...
0
votes
1answer
15 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
0
votes
1answer
25 views

doubt with direction angles

Is it possible for a 3D vector to be drawn with the direction angles of $\alpha=45^\circ$ and $\beta=45^\circ$ ? if yes what is measure of $\gamma^\circ$? I calculated $\cos^2(45^\circ ...
1
vote
1answer
14 views

Get direction of normal without matrix inversion

I am building a 3D engine and I want it to calculate normals for triangles automatically. The user creates a model that is made of triangles. Every triangle is made of three points in the space, and ...
0
votes
1answer
21 views

Reflecting a line from plane

I have a plane given by equation $0=10x+2y-3z$ and a line described by vector with variable $t\ge0$ $(1-t, 1+2t, 1+t)$ How to calculate reflected vector of this line from plane? We treat line as ...
2
votes
2answers
45 views

What makes the inside of a shape the inside?

A question occurred to me when browsing SE this evening, just curious. What specifies the inside of a 3D construct? If I have a hollow sphere, what's to say that the world isn't the inside, and the ...
0
votes
0answers
8 views

Question about the projection of a 3-d region onto the $xz$-plane

How do they get that $D_3$, below? Express the iterated integral as a triple integral: $\int_0^1 \int_0^{x^2} \int_0^y f(x,y,z)\ dz\ dy\ dx$. The projection of the region on the: $xy$-plane: ...
0
votes
2answers
17 views

Coplanarity of two lines in 3D

Suppose we have 2 lines $$l_1 : x = 5 , \frac{y}{3-\alpha}=\frac{z}{-2}$$ and $$ l_2: x= \alpha , \frac{y}{-1}= \frac{z}{2-\alpha}$$ so what will be value of $\alpha$ for lines to be coplaner ? I ...
2
votes
1answer
281 views

Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
0
votes
0answers
24 views

2d to 3d projection problem

I am writing a software where user can add objects in the 3d space and I want to make the user to be able to drag those objects with the mouse. Whenever my mouse moves I have an event fired ...
1
vote
2answers
39 views

Estimating the missing points of a 3D point cloud

Consider a cloud of N points (forming a smooth 3D object), in which n points are missing. Also, consider that there is no prior knowledge about the original shape of the point cloud. The only ...
0
votes
0answers
17 views

Best fitting circle to points in 3D

I have a set of n ≥ 3 points in 3D that are measurements of a possible circle. The measured points are "noisy" so best-fitting algorithms are involved. I'm programming in C# and have put together some ...
1
vote
1answer
36 views

Using several curves in 3D to create a surface

I have a set of several closed curves in 3d (like image below is showing my set of curves from 3 views). To clarify my idea, i ask my questions in two different ways showed by diction 1 and diction ...
3
votes
2answers
44 views

Reflections on a sphere

There is a sphere located in a point s with radius r. The Sphere is a perfect mirror. If i'm sitting in the point c, I want to cast a ray to the sphere such that I hit the point p after bouncing in ...
0
votes
1answer
26 views

Shortest distance between two given lines (Hint)

There seems to be this question that I can't seem to be able to solve. I'm hoping someone could help me figure out how to solve it. Question: Find the shortest distance between the lines ...
2
votes
2answers
34 views

Midpoint of the shortest distance between 2 rays in 3D

I would like to come with an algorithm to find the midpoint of the shortest between 2 rays a+tb and c+sd, where t and s are scalars. I have a scenario which I try to depict like this. One of the ...
3
votes
3answers
147 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 ...