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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1answer
14 views

Paramaterization of paraboloid and plane.

Consider the paraboloid $z=x^2+y^2$. The plane $2x-4y+z-6=0$ cuts the paraboloid, its intersection being a curve. Find "the natural" parameterization of this curve. I have set each equation equal ...
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2answers
19 views

Find the point at which the line intersects the plane. Is the intersection perpendicular?

Find the point at which the line $$x = 1 - t \\ y = 3 + t \\ z = 7 + 2t \\$$ intersects the plane $$x + 2y + z = 20$$ Is the intersection perpendicular? I have found the point of intersection to be ...
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1answer
334 views

How can I transform a 3D triangle to xy plane

Suppose I am given a triangle ABC and its corresponding vertex coordinates in 3D. I want to transform ABC in such a way so that vertex A lies on global (0,0,0) coordinate, B lies on (dist, 0, 0) ...
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1answer
517 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
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0answers
21 views

**Location** of shortest distance between two skew lines in 3D?

I can find the shortest distance $d$ between two skew lines $\vec{V_1}$ and $\vec{V_2}$ in 3D space with ...
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0answers
12 views

Stellating the Octahedron

I am trying to create a very primitive animation/demonstration that shows the stellation of an octahedron to yield the stella octangula. Unfortunately, it seems that the mental image I have for ...
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0answers
9 views

What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
6
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2answers
77 views

Sphere packing question

I'm a secondary school maths teacher, currently on my holidays working through some maths problems for fun. Here is one I have done, but it felt too easy, so if you could check if there's any ...
3
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1answer
31 views

How do I represent a Mobius Band Triangle Parametrically

I am trying to describe a Mobius band in the shape of a triangle like this: parametrically in terms of its $x$, $y$, and $z$ functions. Is this even possible? I know a basic mobius strip can be ...
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2answers
50 views

What are the Eigenvectors in the following matrix?

I have the matrix A: \begin{bmatrix} 4 & 2 & 2\\ 2 & 4 & 2\\ 2 & 2 & 4\\ \end{bmatrix} I found $\lambda I_n - A$ to be: \begin{bmatrix} (\lambda -4) & -2 & -2\\ -2 ...
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1answer
44 views

Determining the angle of a photograph containing known parallel objects/lines.

I have a photograph of a house and a window taken at an angle. I'm trying to determine the angle at which the photograph was taken. The house has wooden siding that can be safely assumed to be ...
4
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0answers
30 views

Finding intersections of tori/toruses

I am looking for intersections of three tori. Is this possible? If so, how? To put things in perspective: I am looking for the coordinates of point P in space, and I have a triangle on the 'ground'. ...
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1answer
34 views

Finding extreme point of a set determined by two planes in $\mathbb R^3$

Problem asks to find a extreme point the set $\{(x,y,z) \mid x-2y \leq 3 , 2y+3z \geq 4 \}$. But I don't think it has a extreme point, because it is intersection of two hyper planes in 3D, which ...
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1answer
403 views

Ellipsoid intersection

Let $E$ be an ellipsoid centered at $p = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a unit sphere. Let $R$ be the ray $p_0 ...
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0answers
15 views

Direction of polyline curvature [closed]

Is it possible to estimate the direction of curvature of a curve or polyline in the 3D case? In the 2D case the description clockwise and counterclockwise makes sense. Is there any notation for these ...
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2answers
2k views

Understanding the Equation of a Möbius Strip

I am in HL Math and trying to finish my IA. My topic is the Möbius band. The only problem is, I do not understand the formula that defines it and everywhere I have looked has just given me a ...
2
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2answers
410 views

Equation of a parabola in 3D space

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is vertex(lowest point) of the parabola. I only know z-coordinate of this point. I need to find coordinates ...
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1answer
24 views

How to get circle points in 3d given a radius and a vector orthogonal to the circle area?

I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector. I got: Angle in degree/radians Circle radius Orthogonal vector I ...
24
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9answers
44k views

Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
0
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1answer
433 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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4answers
2k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in $(x,y,z)$ form, and want to map them onto the plane described by the normal of the triangle, such that I end ...
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2answers
3k views

Point on the left or right side of a plane in 3D space

I have an alpha plane determined by 3 points in space. How can I check if another point in space is on the left side of the plane or on the right side of it? For example if the plane is determined by ...
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2answers
238 views

Calculating spherical distance between two geo-locations

I wanted to show my nephew(16) a simple approach to calculate the distance between two geo-locations. The mathematical knowledge of a 16-year old boy is limited to simple geometrical shapes like ...
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1answer
101 views

Coordinate transformation formula for a pinhole camera model

This is a pinhole camera model (I don't get, is there [R t], or (R, t)). This formula is used to model the projection from a space point M to an image point m. Projection drawing: Tilde over ...
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2answers
201 views

Construct the cross section of a cube by a plane passing through three given points

I want to find/construct the cross section of a cube that includes the three points shown below. In other words, if a plane went through the cube such that it would slice where the points are, what ...
2
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1answer
200 views

Equation of a parabola-shaped toroidal tube with circular cross-sections

I need an implicit function that plots the surface that I am showing you in the picture. Everything you need is shown there. The surface is a tube in the shape of a parabola. The radius of its ...
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2answers
1k views

How can I determine the radius of a dodecahedron?

I am making a dodecahedron that needs to fit inside of a sphere. The sphere has a diameter of 56mm. What is largest possible measurement of one segment of a pentagon side of a dodecahedron that would ...
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1answer
342 views

number of planes possible such that it is equidistant from 4 non coplanar points

If there are for non coplanar points find the number of planes such that all four of them are equidistant from the plane . Sorry one of those problems where dont know what to do . How should i do this ...
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1answer
36 views

Calculating the volume of a surfboard

I'm building a website for a client in which customers can customise the shape of their board (curvature, length, width, thickness, and so forth) and the client has asked if we can calculate the ...
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0answers
235 views

Calculating 3D points corrds from 2D image

The current scenario I have is that I have an image of a rectangular board from an angle and I need to calculate the 4 coordinates of the 4 corners of the rectangle. Currently I have gone through the ...
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1answer
49 views

Small Stellated Dodecahedron, generating triangle vertices

I have been trying to draw a small stellated dodecahedron (would post an image if I had enough rep) using OpenGL, and would like to generate the vertices programmatically. I'm looking for a way to map ...
0
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1answer
14 views

Fit a plane in data set which passes through maximum number of points in this data set and disregards noise

I have a set of 3D points (cartesian coordinates). I want to find the best fit plane. As I understand, there are many algorithms to get a best fit plane. One of them is this by Dan Couture. This fits ...
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2answers
37 views

Showing that the image of a curve lies on a surface?

I am looking for an intuitive explanation to a problem in one of my practice tests. I'm given a parameterized curve from $\Bbb R$ to $\Bbb R^3$, called ${\bf r}(t) = (\sin t \cos t, \cos^2 t, \cos ...
0
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1answer
293 views

Direction Cosines and Rotation Angles

I'm rotating an object in $3D$ space with respect to a relative base, or reference frame. I'm using a normal vector to represent the rotation angles. Suppose you have an object parallel to the ...
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1answer
292 views

Ear clipping triangulation snip calculation

I have a working code of 2D triangulation of a polygon. This uses the following code to detect if a triangle is actually an ear: ...
2
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1answer
401 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 ...
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0answers
27 views

. Find the projection of the triangle on the coordinate planes.

Given the following, three vectors: a⃗ =3i−2j+5k b⃗ =i−6j+6k c⃗ =2i+3j−k Relative to cartesian coordinate systems with origin O. I calculated the sides to be 4.58,11.45 and 7.87. I also calculated ...
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2answers
1k 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
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1answer
23 views

Move point onto circle-outline in R3

I need to do all this in $\mathbb{R}^3$ a plane by $n \cdot p = -k$ a circle within this plane by radius = $r$ and center = $c$ a point $a$ on the inside on the circle (on the plane) a direction ...
2
votes
1answer
420 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 ...
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1answer
15 views

Scaling 3D-Points in Plane

I have some points (3D) all on the same (known) plane. Now I want to scale these points within the plane as opposed to the whole 3D space (as in scalar-multiplication of points in 2D space) Is there ...
0
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1answer
29 views

Calculate 3D Vector out of two angles and vector length

What is the easiest way to calculate vector coordinates in 3D given 2 angles vector length? Input: Angle between X and Y axis: $$\alpha \in [0, 360).$$ Angle between Y and Z axis: $$\beta\in [0, ...
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2answers
44 views

Find closest point on a plane to a given point. Discrepancy with normal vector.

I have a point $(9,5,0)$ and a triangle with points $(1,1,0), (3,3,1), (6,1,0)$, let's label them as $A,B,C$ respectively. In order to get the normal vector, I do the cross product of two vectors. If ...
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1answer
28 views

Get range of 3D object given lowest and highest point and angle

How do you get 3D range of object (highlighted in red below) given its lowest (PL) and highest (PH) (x,y,z) coordinates and orientation of object? Image below is a top view of a box.
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0answers
10 views

3D Linear-geometry with coordinates

Truncated pyramid has a smaller opening with sides ABCD, and a bigger opening with sides FGHE ( where F is o top of A, G on top of B, H on top of C and E on top of D). This figure has 3D coordinate ...
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7answers
917 views

Software to display 3D surfaces

What are some examples of software or online services that can display surfaces that are defined implicitly (for example, the sphere $x^2 + y^2 + z^2 = 1$)? Please add an example of usage (if not ...
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4answers
135 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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1answer
67 views

Intersection of Three Planes proof

I'm supposed to be making a study guide answer for this question, but I'm struggling with proof. Show that the three planes intersect at the point provided that Note that the ...
0
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2answers
31 views

Width of rotated plane

I'm trying to get the width of a rotated plane, but my knowledge of trig functions didn't really help me get what I want. I have a plane, that is $310$ units wide, and is $200$ units away from the ...
0
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2answers
38 views

Final transformation matrix

I have a 3d object, to which I sequentially apply 3 4x4 transformation matrices, $A$, $B$, and $C$. To generalize, each transformation matrix is determined by the multiplication of a rotation matrix ...