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Questions tagged [3d]

For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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About the 3d Surface

I am creating the Enneper Surface in Geogebra with the following equations. Is the surface or equation correct, and does the Enneper surface look like this? I'm confused because Wikipedia has a ...
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1answer
24 views

How can I plot both a point, a plane and a 3D graph in the same plot and manually set my window? [on hold]

I need a visual for my calc for econ major class. How can I plot both a point, a plane and a 3D graph in the same plot and manually set my window?
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1answer
22 views

Finding a third point of a triangle in 3D

I have 3 vertices in 3D: C, P and W. I know: Points C and P and therefore $\overrightarrow{CP}$ and $\overline{CP}$. A direction vector collinear with $\overrightarrow{CW}$ $\overline{PW}$ I ...
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2answers
37 views

Find distance between a line and the origin [on hold]

The given line is defined as following: $$\text{plane 1: } x+y+z = 6$$ $$\text{plane 2: } 2x - y - 5z = -5$$ What is the distance between the line and the origin?
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0answers
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How to determine the position and time of intersection of a moving cone and basic shapes in a 3D environment?

I created a Simulink model in which two objects are moving in a 3D environment (objets have six degrees-of-freedom). The main object has the characteristics of a cone and the second object has the ...
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0answers
29 views

Surface area of part of sphere $x^2+y^2+z^2=a^2$ enclosed by cylinder $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Note the given cylinder $a>b>0$ is elliptical. What I did: I took one fourth of the ellipse in the $xy$-plane and called it $K$, with $$K= \left\{ (x,y):~ 0 \le x \le a,~ 0 \le y \le b\sqrt{1-\...
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0answers
13 views

How can I name data points in scatterplots in Graphing Calculator 3D? [closed]

the title sais it all: I want to visualize datapoints in 3D using Graphing Calculator 3D. Is there any way to name these points? Best Martin
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0answers
23 views

Nonperiodic space-filling polyhedra

For periodic space-filling polyhedra, the maximum number of faces seems to be 38, according to On Space Groups and Dirichlet-Voronoi Stereohedra. For non-periodic space-filling polyhedra, the ...
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0answers
16 views

Sum of sides in a Cuboid

So, I came across this question: What is the surface area of the cuboid C ? (1) The length of the diagnol of C is 5 (2) The sum of the sides of C is 10 Now, if we take the dimensions of cuboid C ...
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0answers
23 views

How to find the location of a point in 3D space from projected 2D angle

I have points $A,B,C$ in 3D space and I know the position of $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. I want to find the location for $C$ given that $AB$ and $BC$ is perpendicular in 3D space but ...
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0answers
23 views

What solid does the truncation of an icosahedron approach?

i was watching some old maths fun related stuff on youtube, and i stumbled across this video: https://www.youtube.com/watch?v=cwWBpjeyRS0 in which the guy mentions how a football is obtained by ...
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2answers
28 views

Find the position vectors of points B and C, both lying on a line, such that the length AB = AC = 10

The position vector of the point $A$ is $2\vec{i} - \vec{k}$ and the equation of the the line is: $$\vec{r} = (-7, 15, -5) + \lambda (3, -7, 4) \ . $$ Find the position vectors of points $B$...
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1answer
97 views

A question about a fly and a spider

A spider is sitting exactly in the middle of one of the smallest walls in a living room, whilst a fly is resting by the side of the window of the opposite wall, 1.5 m above the ground and o.5 m from ...
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0answers
17 views

Distance between a point and a line in space with unknown line equation

We have $A(-2,3,1)$ and we have to find the distance from $A$ to line which contains point $P(-3,5,2)$ and this line makes equal points with coordinate axis. I know how to solve this, I need the ...
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0answers
6 views

How to reconise if my surface is open or closed analitically

I have 2 set of points (point cloud). A it's a cylinder and B it's a half cylinder geometry cut along the long axis ( a junction). I would like to know which of the 2 it's the cylinder and which it's ...
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1answer
63 views

Calculate the path of a string wrapped around 2 cylinders in 3d space

I have 2 cylinders in 3d space. Of each cylinder, I know the origin, the diameter and the normal vector (normal to the circle that defines the cylinder). Now i wrapp a rope from one cylinder to the ...
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1answer
41 views

Probability of line intersecting with randomly scattered spheres.

We have a very big (as in: a unit volume is negligibly small compared to it) volume V, randomly (uniformly and independently) filled with points. The points are the centers of spheres of radius r. The ...
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0answers
12 views

How to move a point [x, y, z] in 3D space around a center [0,0,0], using quaternion readings from a sensor?

I've been browsing the web for far too long, and still can't find a solution to this issue for my student project. Mind you my math skills are not that great, so I'm desperate for any help I can get! ...
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1answer
21 views

$F(\mathbf{x})$ is tangent to $z^2=x^2+y^2$ everywhere

Show the vector field $F(\mathbf{x}) = \begin{pmatrix} x \\ y \\ z \\ \end{pmatrix}$ is tangent to the curve $z^2=x^2+y^2$ everywhere. Geometrically, this is quite straightforward: ...
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0answers
24 views

Shadows of 3d objects on a plane

I know there is another post on this topic; however, I am wondering about this specific question. (I don't know linear algebra, so this might be harder for me) Let's say we have a cube of side ...
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3answers
31 views

Modeling a line in 3D space using length and rotations rather than endpoints

I'm using a cad software which can only create cylinders at the origin based on diameter d and height h. For simplicity sake, in ...
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1answer
16 views

How to move a line defined by Plücker coordinates?

I have a line defined by plücker coordinates L=(U:V). I have a vector A which is perpendicular to the line. I want to move this line following the vector A. I can do this simply by finding two points ...
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0answers
12 views

General formula for rotating a hyperboloid

One of the questions I am having trouble with includes finding the graph of a rotated hyperboloid. The equation is $(x^2)-4xy-2xz+(z^2)=1$. I am having trouble with putting the equation in a way that ...
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0answers
30 views

Find joints positions in 3D robotic manipulator?

I have been trying to solve this 3D mechanics problem, but can't seem to be able to figure out what the best way to do it is. I have this $3D$ robot manipulator with $3$ rotary joints $(B, C, D)$. I ...
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1answer
19 views

3D Axis Rotation & New Value

In a 3D space I want to rotate the origin,just rotating. Let, rotational angles be roll, pitch, yaw. Now let's say I have a vector 0 i+0 j -9.8 k. What will be the value the vector given vector for ...
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0answers
35 views

I need to find a point “D” that lies on the line AB such that the angle between DA and DC is 90 degrees.

I have 2 lines in 3d coordinate system AB and AC. I need to find a point "D" that lies on the line AB such that the angle between DA and DC is 90 degrees. Next might be irrelevant information but: A ...
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2answers
21 views

Finding a vector in 3 dimensions

How could you find a vector if you know the values of another vector and the angle between them in three dimensions? Also, the y component is the same for both vectors and the magnitude of both ...
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1answer
42 views

given $n$ points of human hand throwing a ball find the direction of the throw.

I have the following problem I was given an array of coordinates ($(x,y,z)$) of a human hand throwing a ball in a plane, (first point start of the ball throwing, until the last point which is the ...
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1answer
17 views

Conversion between angle with axis & angle with axial plane

Let's imagine in 3D space I have three angle, $\theta_x$,$\theta_y$,$\theta_z$ respectively with X-axis, Y-axis, Z-axis. Just like $\alpha,\beta,\gamma$ here: I also have $\theta_{xy},\theta_{yz},\...
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1answer
25 views

Direction Ratio of line when one of contributing plane is constant

A line is given by equation $$x-5=5-y, z=5$$ Is the direction ratio of the line 1,1,5? As per my reasoning all points on the line are its direction ratio, so a,b,5 will the direction ratio provided ...
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1answer
48 views

volume of a paraboloid in 3D using integration [closed]

determine the volume of the part of the paraboloid $z=x^2+y^2$ that is below the plane $z=16$. that is, the volume inside the paraboloid. I'm supposed to use double integrals but I'm unsure how to ...
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1answer
38 views

3D point from a know point, distance, angle.

Let's assume I have a point in 3D space A(x,y,z). Two points of distance 'd' from that point A with angle $\alpha$ (with XY plane), $\beta$ (with XZ plane).What are those two points ?
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4answers
38 views

Determine whether the points lie on a straight line.

Determine whether the points $A(2, 6, 2)$, $B(3, 10, 0)$, $C(1, 4, 3)$ lie on a straight line. Is there a formula to solve this question? What is it?
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1answer
17 views

Graphing 3D function

How would I hand-graph a region that is bounded by $z = 6 - 2 x^2/3, x = y^2$, and the $xy$-plane?
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0answers
11 views

Hex map equivalent in 3-dimensional space

In 2-dimensional space, hex maps are great for gaming because any single cell's center is equal distance to any adjacent cell's center, as seen below: I am looking to do a 3-dimensional board game in ...
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0answers
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what is the result type 3D vector, point and scalar arithmetic operations?

I doing programming but I am not good at math. I want to represent point and vector in different type. Both point and vector are tuple of 3 elements, where point represent location and vector ...
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0answers
26 views

Check if 3D Point is below a line

Is it possible to know if a point in below a direction vector or a line? I'm not good at maths and I'm having a really hard time figuring this out, I seen some answers to doing this in a 2D but can't ...
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2answers
35 views

Plane through the intersection of two given planes.

If I have two planes r.n^1 = p1 r.n^2 = p2 If they intersect somewhere then the intersection will form a line, if r' is the position vector of a point on the intersection line then I have ...
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1answer
26 views

How can I check if a sphere collides with a cylinder?

I am working on the following problem: I have a cylinder (of which I know: the radius $r_c$ and points $P_0=(x_0,y_0,z_0), P_1=(x_1,y_1,z_1)$ at the center of the two bases) and a sphere (of which I ...
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1answer
18 views

Finding Overlap of polygons in 3D space

I'm trying to find the amount of "overlap" between two (or more) polygons in a 3D space. The planes all have vector normals pointing in the same direction, so they are guaranteed to be parallel to ...
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2answers
33 views

Finding an equation of a plane through the origin that is parallel to a given plane and parallel to a line.

A plane through the origin is perpendicular to the plane $2x-y-z=5$ and parallel to the line joining the points $(1,2,3)$ and $(4,-1,2)$. Find the equation of the plane. Analyzing this problem I ...
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0answers
27 views

locus of foot of perpendicular in 3 d Geometry

A variable plane cut the coordinate axis at $x,y,z$ axis at point $A,B$ and $C$ respectively such that the volume of Tetrahedron $OABC$ is remain constant and equals $32$ cubic units and $O$ represent ...
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1answer
32 views

Does the line passing through $(3,4,-1)$ which is normal to $x+4y-z = -2$, intersect any of the coordinate axes? [closed]

Does the line passing through $(3,4,-1)$ which is normal to $x+4y-z = -2$, intersect any of the coordinate axes? I'm not sure how to go about this question. Any help would be greatly appreciated. ...
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1answer
71 views

Prove that the straight lines whose direction cosines are given by the relations

Prove that the straight lines whose direction cosines are given by the relations $al+bm+cn=0$ and $fmn+gnl+hlm=0$ are perpendicular if $\dfrac {f}{a} +\dfrac {g}{b} + \dfrac {h}{c}=0$ and parallel if $...
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0answers
10 views

How to Identify the Trace of a Curve as a Point?

I was practicing a question which asked about identifying the traces of a surface in 3-dimensional space. In particular, the surface in question was defined by the equation $$z^2=x^2-2y^2$$ and the ...
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0answers
28 views

3d linear regression line equations

I have a bunch of points in 3D space (around to a survey line). Since only half of the point coordinates were measured, I want to compute a linear regression, from which I extrapolate the other points ...
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0answers
29 views

Fitting a Straight Line to 3D Points, and then finding the nearest point to those lines.

I've been stuck on this problem for over a week now. Essentially, I have a group of 4 tracks of points from a bunch of detectors in 3 dimensions. I need to map these points to straight lines and then ...
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0answers
26 views

best way to plot the 3D shape made by many intersecting f(x,y,z) functions?

What's the best way to use a computer to plot the 3D shape made by many intersecting f(x,y,z) functions? I was trying to do something like the following, except I still have not idea what the shape ...
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0answers
61 views

Volume of cuboid with unequal heights [closed]

Can you find the volume of a cuboid which has different lengths for every edge? Is there a way to calculate it accurately or do I need to use numerical methods?
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1answer
24 views

How to create a Quaternion rotation from a forward- and up- vector? [closed]

I need the rotation Quaternion of an object, I have it's foward and up directions (as 3D vectors), so I thought it would be easy to create a Quaternion rotation from that, but I can't seem to get it ...