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

0
votes
1answer
286 views

How do you get 3D gradient direction and magnitude?

I know that we can get the magnitude and direction from 2D gradient ? 1) mag(Gx,Gy) = sqrt ( Gx^2 + Gy^2 ) 2) angle(Gx, Gy) = tan^-1 (Gy/Gx) What about in ...
5
votes
0answers
37 views
+100

Is there a generalization of the Lagrange polynomial to 3D?

What is a way to construct a smooth polynomial surface ($\mathbb{R}^2 \rightarrow \mathbb{R}$) with Lagrange-polynomial properties in every partial derivative? I want to try this for image ...
2
votes
0answers
11 views

Rotating a point in space about another via quaternion

I have a system that is giving me a point in 3D space (call it (x, y, z)) and a quaternion (call it (qw, qx, qy, qz)). I want to create a point at (x+1, y, z), and then rotate that point using the ...
0
votes
1answer
25 views

Z coordinates of 3rd point (vertex) of a right triangle given all data in 3D

this is my first post.. I hope this good I have 1 triangle in space (3D)... and I know all data except the coordinates of 3er point(vertex)... for example this: then: ...
3
votes
1answer
314 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 ...
1
vote
1answer
331 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 ...
1
vote
1answer
63 views

Looking for help for building a Spline's algorithm 10th order

I'm trying to code the following algorithm in C++ and need help to understand the build of Splines from a mathematical point of view (found on page 129 on this paper). $$ f(t) = \boldsymbol{t} \cdot ...
2
votes
2answers
130 views

How can I convert camera motion into zoom?

I try to reconstruct a camera of a video sequence via match moving techniques. After the reconstruction process all seemed to work as expected, but then I've realized my camera is moving forward ...
2
votes
1answer
24 views

What is the difference between coordinates transformation and change of coordinates?

In the context on 3D computer graphics, what is the difference between coordinates transformation and change of coordinates? It can just be a matter of notation, but my book makes a clear distinction ...
1
vote
2answers
45 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 ...
0
votes
1answer
24 views

Plot a set, given in cylindrical coordinates, with Maple and $\text{plot3d}$

I want to plot the set $\phi(A)$ with Maple, where $$\phi:[0,\infty)\times[0,2\pi)\times\mathbb{R}\to\mathbb{R}^3\;,\;\;\;(r,\phi,z)\mapsto(r\cos\phi,r\sin\phi,z)$$ is the transformation in ...
0
votes
0answers
30 views

Show that circle generates the surface $(x^2+y^2+z^2)(\frac{x^2}{a^2}+\frac{y^2}{b^2})=x^2+y^2$

$POP'$ is a variable diameter and the ellipse $z=0, \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and a circle is described in the plane $PP'ZZ'$ on $PP'$ as diameter. Prove that as $PP'$ varies, the circle ...
-1
votes
0answers
27 views

walking in 3Dimension [closed]

Starting from $(0,0,0)$ of a moving object in the coordinate space through a series of steps, each step of length one. Each step to the left, right, up, down, forward or backward with equal ...
5
votes
3answers
22k 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. ...
2
votes
0answers
60 views

Is this a legit way to visualize complex functions?

I am doing laplace transform in a class and I hate how there seems to be no graphical support when things are transformed to laplace domain i.e. nobody cares what they look like in laplace domain But ...
5
votes
4answers
156 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
30 views

How to sketch the level curves of $f(x,y) = x^2 - y^2$

I've been practising functions of several variables for college and I've been working with circles all the time $(x^2 + y^2)$, however, I still can't figure out how to solve non circular shapes, as ...
1
vote
1answer
47 views

Transforming coordinate system vs objects

In computer graphics it's pretty common to assume the camera is always positioned at the origin and oriented in one direction. In case we want to move the camera closer to an object in the world ...
1
vote
1answer
43 views

How did the author find the vector v prime perpendicular to n

I'm reading the $3D$ Math Primer for Graphics and Game Development by Fletcher Dunn and Ian Parberry, but I've gotten stuck. If you look at the attached image where it says, "Now we can see the ...
0
votes
1answer
392 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
0answers
17 views

How do you interpret this 3D function: Z = EXPX (a,b) * EXPY (1,c)

I have fitted a curve to my data using TableCurve3D software. The best graph which fits my data almost perfectly is Z = EXPX (a,b) * EXPY (1,c). Note that "a", "b", and "c" are constants. The problem ...
1
vote
1answer
56 views

Rotating an object correctly when you can only rotate world axis.

This question may be useful to some people, but it is not posed correctly for my particular situation, please see: Simulating simultaneous rotation of an object about a fixed origin given limited ...
1
vote
1answer
41 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 ...
0
votes
1answer
686 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 $T$?
1
vote
1answer
34 views

Help me find the function behind this data?

I have a function $f(x, y)$ and I have another (non-mathematical) algorithm capable of inefficiently generating the exact same results as in in a 'brute force' manner. Since I have been able to find ...
0
votes
1answer
276 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 ...
13
votes
8answers
27k views

Recommended (free) software to plot points in 3d

I am looking for (preferably free) software to: 1) plot 3d points read from a file. A scatter plot would be fine. 2) Optionally color the points by a property - also read from the file It would be ...
1
vote
1answer
48 views

Arc length of a 3D Curve

I have a set of points in 3D space: $$\left(x_i, y_i, z_i\right)$$ These points create a 3D curve and I am trying to calculate its arc length. I have followed what is described here but when I ...
1
vote
2answers
33 views

How to determine the distance to one point from another in a 3D coordinate system?

I wonder how I can calculate the distance between two coordinates in a $3D$ coordinate-system. Like this. I've read about the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ (How) Can ...
3
votes
2answers
78 views

Why is the volume one third of that? I mean, where's the fault in my logic? [duplicate]

The volume of a cuboid is $l \times b \times h$. That is, it is equal to base area times height. I think it means that the base is added up height times, it becomes volume (It makes sense if we think ...
0
votes
3answers
43 views

Finding Tangent Line to Graph

Find a vector equation for the tangent line to the curve of intersection of the cylinders $\ x^2 + y^2 = 25$ and $\ y^2 + z^2 = 25$ at the point (3,4,2). I don't understand the answer key. I've ...
0
votes
1answer
14 views

Velocity vector transformations with respect to a global frame of reference

This seems like it should be a simple problem, but I've been stuck on it for about a day now. It's technically a programming problem, but I'm posting it here because the root of the problem is really ...
0
votes
0answers
14 views

How do I generate a Spotlight Projection Matrix for Shadow Mapping?

I'm currently in the Process of making a simple little shaodw mapping ystem for Ogre3d. I'm currently stuck at Mapping the Shadow map texture to the object for depth comparison because I have no idea ...
0
votes
1answer
65 views

Point inside a tetrahedron joined to corners creates how many new internal planes?

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? How do we ...
1
vote
0answers
21 views

Sections of cones in higher dimensions

Everybody knows that when a plane intersects a cone at different angles and positions, we get conic sections. But, I wanted to know that if the same was possible in higher dimensions. If we take the 4 ...
2
votes
1answer
288 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
1answer
16 views

Descretizing an arbitrary plane in 3D

I have a plane in 3D with size $L1\times L2$ with arbitrary orientation. The normal to the plane is $\vec{n}$. I am trying to descretize this plane into $N1\times N2$ grids. I want to have the ...
0
votes
2answers
81 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 ...
1
vote
1answer
30 views

Curve on a torus

Consider a curve $f$ that connects two arbitrary points on a torus. What are the equations that defines the curve $f_{min}$ whose such a distance is minimal?
1
vote
1answer
28 views

Can a 1-side, 1-border object exist in 3D?

We are three friends discussing whether a three dimensional object with a single side and a single are can possibly exist. I first came up with a Moebius strip as an affirmative example The second ...
0
votes
1answer
34 views

Understanding normal and binormal of a vector or of a spline

I found a paper where it computes the 3D trajectory of a quadrotor and defines an error position as the difference between 2 vectors (here the source, under 3D trajectory control): $$ e_{p} = ...
0
votes
2answers
48 views

Stuck on a 3d equation

I have three 3D points with an known Z value: point 1 = (0, 0, Z1) point 2 = (64, 0, Z2) point 3 = (64, 64, Z3) I need an equation to solve for the Z value given ...
1
vote
1answer
54 views

Linear equations in 3D space [duplicate]

I need to search a line in a 3D space. I have a starting point (coordinates) of the line and the angle at which it is suppose to go (relative to each of the axis). I need to start from the starting ...
2
votes
1answer
26 views

Hyperbolic paraboloid: how to find the distance from a point on the surface to the $z$-axis?

The given hyperbolic paraboloid is $z=xy$. How do I find the distance $r$ from a point on the surface to the $z$-axis? I used a function grapher to visualize the 3-D surface. But I am unable to ...
3
votes
3answers
94 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
40 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 ...
2
votes
1answer
71 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
28 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
24 views

Non-standard 3D rotation of a set of points [duplicate]

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
45 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 ...