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.

learn more… | top users | synonyms

1
vote
5answers
314 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
1answer
22 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
0answers
25 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, ...
0
votes
0answers
12 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: ...
2
votes
2answers
51 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
1answer
29 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 ...
0
votes
1answer
30 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 ...
0
votes
2answers
33 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 ...
0
votes
1answer
131 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
121 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 ...
1
vote
2answers
59 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 ...
12
votes
1answer
217 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
1answer
38 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 ...
5
votes
4answers
180 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 ...
2
votes
2answers
78 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 ...
1
vote
2answers
29 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 ...
1
vote
1answer
70 views

How to draw or plot illustrative figures?

stackexchange users I would like to plot or draw some illustrative figures for my research paper. I've tried GeoGebra already. But couldn't draw them as I wanted. So my question is How can I draw ...
1
vote
0answers
103 views

Triple integral, finding the volume between two planes and a surface in 3D

So I have tried to solve this problem, but I'm running into a problem, because the top circle (intersection of the function with z=1) when you project it onto the xy plane is smaller than the circle ...
0
votes
0answers
22 views

How to do the calculation of the error in positioning in 3D Space?

I'm mathematically calculating a position on given data in a program. But I need to validate that the calculated values against the original position value. If the Original position is Xi,Yi and Zi ...
5
votes
0answers
66 views

From Icosahedron to Pentagonal hexecontahedron (Floret Tessellation)

Inspired by this post: Floret Tessellation of a Sphere I tried to transform myself an icosahedron into its simplest Floret tessellation. But I am having trouble when applying the 'method' given in the ...
0
votes
0answers
34 views

Unique representation of each point in 3d space by Linear combination of 3 mutually perpendicular vectors.

I intuitively accepted that there is an unique representation of any point in a 3d space by linear combination of 3 mutually perp. vectors. But now I'm wondering is this an axiom or a theorem? If ...
0
votes
1answer
39 views

Flatten 3D VectorA so it's perpendicular to VectorB

Basically I have 2 3D vectors: Vector A (green) and vector B(red). I need to calculate a third vector that is perpendicular to VectorA (green) but points in the same direction than VectorB (red). ...
0
votes
0answers
34 views

Inertia tensor of a triangle in 3d

I am computing inertia tensor of a triangle given by its 3 vertices. The tensor should be computed at some local origin. I used covariance as explained in this Wikipedia article, but I am not sure ...
0
votes
0answers
150 views

3D equation of a cone-like shape

Imagine there are two parallel planes (base plane and plane1) in the following image: There is one point on the base plane and there are several points on the plane1. The positions of these points ...
1
vote
1answer
105 views

Is it true that a arbitrary 3D rotation can be composed with two rotations constrained to have their axes in the same plane?

I am interested in decomposing an arbitrary rotation in 3D space into the product of two rotations which are constrained to have their axes in the same plane (for instance x-y plane). Statement of ...
0
votes
0answers
24 views

What the Surface function will it be if a circle tilted with an angle and then rotating around z axis

My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from ...
1
vote
0answers
32 views

unique cube arrangments

i have received this math riddle which i cannot solve, the riddle: given a set of cubes, a unique shape is any shape that was created joining cubes sides together and does not match any previously ...
0
votes
0answers
31 views

An example of a space curve with given normal and osculating planes

I am student currently taking calculus 3 and I recently was given a quiz with a very difficult question. The question relates to the chapters in my book which talk about "Arc Length and Curvature" and ...
1
vote
1answer
20 views

Intersection between two surfaces

Find Find parametric equations for the tangent line to the curve of intersection of $z=x^2+y^2$ and $6x^2+5y^2+3z^2 =23$ at $(−1, 1, 2).$ I tried plugging in $z=x^2+y^2$ in the second equation to ...
1
vote
0answers
57 views

How to determine 3d measurements

I am trying to reproduce an artwork that is both a 2D drawing and 3D paper sculpture by Romanian artist Liviu Stoicoviu done in the 80s, The Triangle: I have tried to trace the 2D artwork which ...
0
votes
1answer
33 views

finding two most distant 3d points

I'm trying to write an algorithm. There are 9 points 3 of x ,3 of y,3 of z. How can I find the two most distant? Mathematically, I need explanation. Thank you for all appreciated answers. coordinates ...
1
vote
0answers
49 views

What function has a 3D graph that will look like a spiral into a singularity?

I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint. I think a function that defines a black hole/singularity surface might look something ...
2
votes
2answers
14 views

Equation of line gives equation of plane

Given a 3D line in parametric form $$x = 5 + t$$$$y = 1 +3t$$$$z = 4t$$ I did the following calculation: $$x + y + z = (5 + t) + (1 + 3t) + (4t)$$ Therefore $$x + y + z = 6 + 8t = 6 + 2(4t) = 6 ...
1
vote
2answers
28 views

How to determine the increase in the Z-Axis. Of a tessellated sphere

I have been tasked with drawing the sphere below for a programming assignment using openGL. I have the assignment mostly completed however I am having issues figuring out the math for the sphere. For ...
0
votes
0answers
20 views

Check if an axis aligned bounding box intercepts with a triangle

As the questions says I am trying to check if an AABB intersect with a triangle. I've divided the problem in 3 parts: check if any of the triangle edges intersect any of the AABB faces check if the ...
0
votes
1answer
21 views

Given unit quaternions $q_0,q_1$, find $q$ such that $q_1 = q^* q_0 q$

I rotate an object in space and find two orientation (unit) quaternions. $q_0 = {}^{M_2}_{M_1} q$ is the orientation at the 2nd position relative to the 1st position, measured in frame M. $q_1 = ...
0
votes
1answer
19 views

3D Vector Equation

Consider the points $A (1, 5, 4)$, $B (3, 1, 2)$ and $D (3, k, 2)$, with $\overline{AD}$ being perpendicular to $\overline{AB}$. (i) Find $AB$ (ii) $AD$ , give the answer terms of $k$. Show that ...
0
votes
1answer
62 views

Spherical Sector Volume

I'm trying to find the volume of a spherical sector without knowing the height of the cap. Wikipedia provides this formula: And says: "where φ is half the cone angle, i.e., the angle between the ...
0
votes
1answer
22 views

$5$ General Planes make how many CLOSED SPACES?

Actual problem is How many spaces $5$planes divide a space into? and by some analogy and proof, I found that $5$planes divides a space into $26$spaces. in fact, I considered first "How ...
1
vote
1answer
43 views

Distance between two skew lines

I have 2 skew lines $L_A$ and $L_B$ and 2 parallel planes $H_A$ and $H_B$. The line $L_A$ lies in $H_A$ and $L_B$ in $H_B$. If the equations of $H_A$ and $H_B$ are given like this: $x+y+z = 0$ (for ...
0
votes
1answer
84 views

Calculate X Y Z from two specific degrees on a sphere

I am a programmer, don't know much about advanced math. I would need the exact formula(s) that could achieve this, so I can translate it to my programming language. I am having a headache trying to ...
0
votes
1answer
26 views

Calculate projection of a line in a square

Said that we have two points (P1, P2) that form a line, and 3 points (S1,S2,S3) that form a square, how would we calculate the position X and Y of the point resulting from the intersection of the line ...
0
votes
2answers
46 views

Find 3rd point in 3D space based on position of 2 points

Assuming i have 2 points $P_1$ and $P_2$ having coordinates of $P_1 = (x_1, y_1, z_1)$ $P_2 = (x_2, y_2, z_2)$ I want to find the coordinates of a 3rd point ($P_3$) where it creates a straight line ...
0
votes
3answers
46 views

Definite method for finding the intersection of two cartesian lines in 3D.

I have the following problem: Determine if these lines intersect. If so, find their point of intersection. $L1 = (4,5,-1)+t(1,1,2)$ $L2 = (6,11,-3)+s(2,4,1)$ I managed to solve this ...
1
vote
2answers
58 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 ...
1
vote
2answers
82 views

How to check if a 3D line segment intersects a cylinder?

I have developed a check for a 2D case of a circle intersecting a 2D line segment, however there is a particular case that I can't figure out how to extend to 3D: If one endpoint on the 3D line ...
-1
votes
6answers
36 views

Finding the length from a point to a line in 3D??

Here is the question: What is the distance from the point $(4,1,-2)$ to the line given by : $$x=2+t$$ $$y=3+3t$$ $$z=4-t$$ Help would be greatly appreciate, as i do not even understand where to ...
0
votes
1answer
685 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 ...
0
votes
2answers
55 views

Configuration of five or more mutually equidistant points in space.

How is it proved that there is no configuration of five or more mutually equidistant points in $R^3$? Is it done by induction? I'm stuck. Help would be appreciated. Well, surely equilateral ...
2
votes
0answers
67 views

Beautiful problem about polyhedrons [duplicate]

A regular tetrahedron has this property: For any two of its vertices exists a third vertex, which forms a regular triangle with these 2 vertices. (But it doesn't mean any 3 vertices form a regular ...