Tagged Questions

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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0answers
16 views

Why is tree traversal the fastest ray-box method?

I'm learning ray tracing (the problem of intersecting a ray, aka a vector, against a 3D box defined by a max and a min point) and I'm wondering: why is a tree traversal (e.g. bounding volume ...
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1answer
85 views

How to rotate a 3d vector to be parallel to another 3d vector using quaternions?

I have a vector (a,b,c) and another vector (d,e,f). I'm trying to rotate (a,b,c) so its parallel to (d,e,f) using quaternions. I need help understanding how I would do this. I have so far that a ...
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1answer
49 views

Find vector rotated on 3D plane

I don't have access to a computer so I can't give pictures but I will try to make this easy to visualize. Suppose I have a vector $n$. I will now draw a plane normal to this vector that and have that ...
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1answer
57 views

clockwise or counter clockwise in 3D

I have two different situation that I need to make distinction between them (shown in the picture). In other words, in (A) points 3 and 4 are in right and left side of line 1-2. However, in case (B) ...
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1answer
228 views

Find a 3D vector given the angles of the axes and a magnitude

I would like to know how one would find a point from the angles of three axes and a magnitude. I know how to do this in 2D: $(\cosΘ * m, \sin(Θ) * m)$. However, I would like to know how this would be ...
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1answer
98 views

texture mapping from a camera image to a 3D surface acquired by a kinect

I have the following problem: A kinect camera capture a 3D surface and save it as a .obj files containing all the positions of the vertices (in the kinect coordinate system). If I take a picture ...
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2answers
65 views

Find the relation between the volumes of a cone and inscribed sphere

I have a question that I've been working upon for a long time but in vain. Can you help me. Determine the relation between the volume of a con circumscribed to a regular tethadron and the volume of a ...
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0answers
37 views

Shooting a grenade - angle throwing

In my 3D simulation/game I need to shoot a grenade from a grenade launcher. The movement of the grenade is already setup by someone else. all I need is to give him the pitch angle of the grenade ...
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1answer
115 views

Area of circle formed when sphere is sliced by a plane

First off, when a sphere is cut by a plane, is a circle always formed or does a ellipse get formed in some cases? If a circle is always formed, how do you prove it? Next, how would you find the area ...
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0answers
72 views

Distance from a point to the walls of a cube in 3D

I have defined six different planes that constitute a cube($6$ plane equations). I place an object within the cube at a point $P_1 \equiv (X_c,Y_c,Z_c)$. There are $6$ cameras on the object pointing ...
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0answers
88 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
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0answers
36 views

Partition of the 3d space with circles?

Does it exist a partition of the 3d space with circles of positive radium? I know the answer is no for a plane, but I can not transpose my demonstration to the space and I have no clue on how to do ...
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3answers
49 views

Determining if a point is inside two planes

I have two planes(Plane 1 and Plane 2) the normals ($n_1$ and $n_2$) of which are known to me. How do I determine if a point is inside the two planes? By inside I mean the 3d space between Planes 1 ...
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2answers
176 views

Finding distance between lines in 3D

Find the distance between the lines $L1$ and $L2$ where $$L1: \frac{x-1}{2}=\frac{y-2}{-3}=\frac{z-3}{4}$$ and $$L2: \frac{x+1}{3}=3-y=\frac{z+5}{5}$$ I need to first show that the lines are skew and ...
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1answer
30 views

Linear Algebra: finding specific linear combinations which meet the criteria

Consider any three vectors u,v,w in 3-dimensional space s.t joining the three vectors by straight lines forms a triangle. Under what condition on c,d,e will the combination cu + dv + ew fill the ...
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1answer
20 views

This is regarding 3d parametarization and vectors.

Generally, I have a hard time conceptualizing how to sketch a vector that looks like $(\cos t, \sin t, t)$. How do I approach this? Usually, in an examination, there are really small bounds given so ...
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1answer
460 views

How to find out if four points are on the same plane, only by using distances?

There is a method called Cayley-Menger determinant in order to find if 3 points are collinear, 4 points are coplanar etc. provided that all the pairwise distances are given. However, in 2-D, there is ...
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0answers
140 views

Find the linear (vertical) acceleration using a three axis accelerometer.

I genuinely apologise for what may be a poorly worded question. I'm extremely tired but have a ridiculous huge and important project due in on Monday for my degree. Thank you in advance for any help ...
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0answers
30 views

What is the offset curve of a 2D slice of the 3D offset of a twisted swept figure

I have a simple 2D shape as below helically swept. I then do an offset in 3D from the surface. to get if I take a 2D cross section I then get As you can see the offset curve of the 2D ...
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0answers
37 views

How to define a binormal equation using 3D coordinates, with given sine wave function?

I am attempting to implement in code the math and functions found here: http://http.developer.nvidia.com/GPUGems/gpugems_ch01.html So this question is contextual to that article, I'm sorry for that, ...
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2answers
40 views

Scale a Point onto Plane

I'm trying to find the scale factor that scale a point onto plane in 3D Space. I have the following information: Point on a plane: $a = (x_1,y_1,z_1)$ Plane equation: $P\colon Ax + By + Cz +D =0$; ...
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1answer
47 views

How to Create a Plane Inside A Cube

I have a $e \times e \times e$ cube and I want to create random planes with equation $ax + by + cz + d = 0$ inside this cube. I will put random points on those randomly created planes as well. Here ...
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1answer
52 views

Equation of a plane through intersection of two and parallel to other

I have got two planes $$x+y+z=1$$ and $$2x+3y-z+4=0$$ . I am required to find a plane by intersection of two and parallel to $x$ axis . I think the plane parallel to $x$ axis so Simply $P1+kP2=0$ ...
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3answers
72 views

3D triangle computer graphics

We are given a 3D triangle with vertices $(0,0,0), (5,0,10), (0,20,0)$. What is the $z$ value of the point in the triangle with $x=3, y=1$? How do we find the $z$ value?
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1answer
406 views

Best way to plot a 4 dimensional meshgrid

I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown ...
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1answer
73 views

3D Graphing--finding an equation given a graph

I'm having trouble finding a reasonable equation for this graph: http://i58.tinypic.com/15gtrn7.png The x axis is the horizontal, y-axis is the axis coming out of the screen, the z-axis is vertical. ...
2
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0answers
104 views

Best closed convex surface fitting N points in 3D

First. It's easier to understand the problem by describing the application where it arises from. We have a convex body $B$ in $\mathbb{R}^{3}$ and measure points on its surface. The measurements are ...
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0answers
73 views

Solve equation for best fit plane

It was posted by joriki that "Subtract out the centroid, form a 3×N matrix X out of the resulting coordinates and calculate its singular value decomposition. The normal vector of the best-fitting ...
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1answer
47 views

Classifying point stabilizers for the groups associated with 3D model geometries.

For those who have the book, this question is regarding p181 in Thurston's "Three Dimensional Geometry and Topology" (although I will do my best to summarize it). Basically, there's an entire ...
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1answer
47 views

Find $z$ of a point in a plane in 3D space

Say for example, I have 4 points which I know the coordinates to, how can I find a fifth point that lies somewhere within them? E.g, if $A(0,0,a)$, $B(1,0,b)$, $C(1,1,c)$ and $D(0,1,d)$ lie in a ...
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2answers
101 views

How to Represent a 3D Line under Polar Coordinates

In one of my applications, I need to represent a line under 3D polar coordinates system. In 2D, we can define a line by a distance to the origin and then a angle indicating the direction of the line ...
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1answer
95 views

Big axis of an ellipse

I drew a circle in this square and I transformed them (view in 3d). How to find the angle between the big axis and $y$ or $x$ axis? Blue plane rotated by 36° around $y$ axis; azimut is 30° and ...
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2answers
326 views

Find tangent vector to surface given a point on the surface and its normal vector (for a sphere)

I need to know how to find a tangent vector to a point on the surface of a sphere if I am given the point P and the normal vector at that point N. I know that there are many possible tangent vectors ...
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2answers
42 views

Problem with vector multiplication

I have this plane problem and the answers are released for it. I don't understand this specific part: Why does : (i + 4k) x (3j - k) = -12i + j + 3k. I tried using the cross product method, however, ...
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2answers
92 views

solving 3-d coordinates from x, y and z distance

I working with WiFi positioning and i want to know the exact coordinate where I am. Here is the problem..
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2answers
154 views

What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...
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0answers
87 views

Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
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0answers
49 views

How many edges is sufficient to check to prove polyhedron convexity?

Consider the set $\{u_{1}, u_{2}, \ldots, u_{n}\}$ of points on the spere in $\mathbb{R}^{3}$ (i. e. $||u_{i}|| = 1$) and their convex hull C = $Hull(u_{1}, \ldots, u_{n})$. It's obvious that each ...
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1answer
70 views

Rotate the Points on a Plane $P = ax+by+cz + d = 0$ parallel to $z = 0$ plane

I have a plane $P = ax+by+cz + d = 0$ and many points on that plane. I want to rotate $P$ so that it becomes parallel to $z = 0$ plane. Which method should I use? I know that the normal vector of my ...
4
votes
1answer
101 views

Any interesting properties of Fermat's Last Theorem Surfaces?

I wonder if there are any interesting geometric (as opposed to number-theoretic) properties of what might be called Fermat's Last Theorem surfaces, i.e., $x^d + y^d = z^d$. Below are the surfaces for ...
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0answers
27 views

Taking into account Camera Direction in 3d models using Trig

I have been working on a 3d rendering project as code. I am a bit stumped on the math though. I know how to render points using arctangent on an HTML canvas using JavaScript, like this: ...
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1answer
88 views

Rotation formalisms in three dimensions

I'm little bit confused. The Rotations are described by various means Direction Cosines Matrix (DCM); Euler Angles; Euler Axis/Angle; Quaternion. What is the difference between them. How I can ...
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1answer
40 views

Finding points on a segment representing a 3D angle

I'm trying to calculate multiple points on an angle (circle segment) so that I can store it as a VBO of Vector3 and render it in OpenGL. Imagine each of those points on the dotted line as a ...
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2answers
102 views

2D data fitting

I have some numbers as a function of 2 variables: $(x, y) \mapsto z$. I would like to know which function $z=z(x,y)$ best fits my data. Unfortunately, I don't have any hint, I mean, there's no ...
2
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1answer
214 views

How To Generate Random Points on the Positive Side of a Plane in 3-D

Edit: The question can also be interpreted as: How to generate random coplanar points in a cube? Here is what I am struggling with: I have a cube, whose origin is $(0,0,0)$ and one edge length ...
3
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1answer
90 views

Check if a point is on a plane? (Minimize the use of multiplications and divisions)

In $\mathbb R3$, given a plane $\mathcal P$ defined by three 3D points points $v_0, v_1, v_2$, I want to check if another point $p$ belongs to that plane, while avoiding the use of multiplications and ...
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1answer
86 views

How to generate a 3D spherical symmetric object from a 2D circular graph

I have a very simple 2d graph. 6 lines separated by equal angle of 60 degrees radiate from the center of a 2d circle, intersecting with the circumference at 6 points. Suppose I know the coordinates ...
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0answers
27 views

Possibility of 3D interpolation without decouple axis

I am wondering if it is possible to do 3d spline interpolation without decoupling the axis. Such as creating a spline function on x then a different one on y and another on z. Then for any given ...
2
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1answer
104 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
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1answer
204 views

How to find the curve of intersection of a ellipsoid and a plane?

Let $C$ be the curve of intersection of the ellipsoid $x^2+2y^2+3z^2=39$ and the plane $3x+y-7z=0$. Find the parametric equations for the tangent line to $C$ at $(5,-1,2)$. I don't know how to find ...