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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2answers
277 views

Plane that passes through the point (−3, 2, 1) and contains the line of intersection of the planes x + y − z = 4 and 4x − y + 5z = 2

Find an equation of the plane. The plane that passes through the point (−3, 2, 1) and contains the line of intersection of the planes x + y − z = 4 4x − y + 5z = 2 I know the normal to plane 1 is ...
-1
votes
2answers
184 views

Finding Equation of a Plane through the origin and the points$ (1, −2, 5)$ and $(8, 3, 2)$

Find an equation of the plane. The plane through the origin and the points $(1, −2, 5)$ and $(8, 3, 2)$ I know $AB$ is $<7,5,-3>$ but I don't know what to do after that
7
votes
2answers
92 views

What's the “easiest” closed 3-manifold with a nonabelian fundamental group?

I'm looking for some easy compact, oriented 3-manifolds without boundary that have a nonabelian fundamental group. It needn't be perfect. "Easy" means that it has an easy Heegard diagram, say, one ...
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votes
1answer
19 views

Which of the surfaces does the vector lie on?

So I used the trig identity (y^2 + z^2 = 1) on my y and z component. So I concluded that the cylinder y^2 + z^2 = 4 satisfies the question. I also concluded that the plane x + y = 3 satisfies the ...
1
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0answers
96 views

Catenary equation in 3D

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is lowest point of the catenary curve. I only know z-coordinate of this third point. I need to find ...
2
votes
2answers
413 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 ...
1
vote
1answer
128 views

Creating a 3D Plane using the normal and point vector

I'm not understanding the relationship of a normal vector and a position vector that makes it into a 3D plane, and how I can visualize what that 3D plane is going to look like in 3D space. Say I ...
0
votes
1answer
37 views

Describing the shape of a level surface given functions

(1) Describe the level surfaces of $f(x,y,z) = sin(2x+y-z)$. For what values of 'c' do level surfaces exist? For this one I set the function equal to c and tried to put it in a more manageable form. ...
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votes
2answers
21 views

Find an equation of a plane

Find an equation of a plane which contains the points: $(0,0,3),(3,2,1)0$, and $(6,2,0)$ I know I need a vector in order to use the equation $d=ax_0$+b$y_0$+c$z_0$ Now, could I just select any two ...
0
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2answers
24 views

Give parametric equations for the line in 3 space

Give parametric equations for the line in 3 space which goes through the point (1,2,3) and is parallel to the line given by the symmetric equations: (x-1)/-1 = (y-2)/3 = (z-2)/1 So, based off those ...
1
vote
3answers
49 views

Parametrization of the intersection of two given surfaces

Find a parametrization of the intersection between the two curves $z=x^2-y^2$ and $z=x^2+xy-1$. I figure I should set them equal to each other but I'm not sure where to go from there: $$x^2-y^2 = ...
1
vote
0answers
58 views

Calculating Normals across a sphere with a wave-like vertex shader

This is a bit of a CS question, but more than not it's a 3D math problem. I've been trying to get the correct normals for a sphere I'm messing with using a vertex shader. The algorithm can be boiled ...
2
votes
1answer
41 views

Finding the unit normal vector

Q. Consider the following vector function. $$ r(t)= \langle 6\sqrt{2}t,e^{6t},e^{-6t} \rangle $$ Find the unit tangent and unit normal vectors T(t) and N(t). I found $$T(t)= ...
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0answers
44 views

Is $y=5 $ a plane in $\Bbb{R}^3$?

I suppose it depends on how you define the variance on $x$ and $z$, but this question seems simple to me: yes. If $P(x,y,z)$ is the set of all points $x, y, z$ such that $y=5$, it seems clear that ...
0
votes
0answers
15 views

Randomly distribute objects over a surface with some clusters

I want to randomly distribute some(in thousands) objects over a surface. This I can achieve with a function say x,y = rand(). This will evenly distribute objects over the surface, but is it possible ...
1
vote
1answer
569 views

What is the line of greatest slope on a plane?

Let $P$ be a plane in $\mathbb{R}^3$ that is inclined (neither horizontal nor vertical). When considering lines lying on $P$, it is sometimes said "$L$ is a line of greatest slope of $P$". What is ...
2
votes
0answers
84 views

Rotate a 3D Vector onto Another 3D Vector

I am trying to transform one triangle onto another triangle in 3D space (Right Triangles). My thought was I align the forward and left vectors, then translate the center of one to the other. ...
2
votes
0answers
17 views

Find a vector equation and parametric equations for the line segment that joins $P$ to $Q$. [duplicate]

Find a vector equation and parametric equations for the line segment that joins $P$ to $Q$. Here $P(1,-1,7)$ and $Q(7,5,1)$. I have tried to find $r(t)$ by using the formula $r(t)=p+t(p-q)$ but ...
2
votes
2answers
105 views

When the intersection between a sphere and a cylinder is planar?

We have a sphere and a circular cylinder. Let the sphere center be $O$ and radius $R$, and the cylinder axis $a$ and radius $r$. I solved the specific case intersection graphically on 2 planar ...
0
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2answers
48 views

does anyone know how to graph $x^2+2y^2+3z^2=12$?

I just can't think of how I should draw this graph in 3 dimensions. Can anyone draw a graph for this?
1
vote
1answer
59 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
204 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: ...
4
votes
2answers
467 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 ...
0
votes
1answer
56 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 ...
3
votes
0answers
151 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 ...
0
votes
1answer
182 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
71 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
52 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 ...
1
vote
1answer
47 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 ...
1
vote
1answer
123 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
2answers
91 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
148 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 ...
7
votes
3answers
471 views

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 ...
3
votes
1answer
111 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
1answer
80 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 ...
0
votes
1answer
42 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 ...
2
votes
2answers
149 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 ...
0
votes
3answers
334 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 ...
2
votes
1answer
56 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 ...
0
votes
1answer
18 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 ...
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vote
1answer
45 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
43 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
3answers
52 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
2answers
51 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 ...
0
votes
1answer
111 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} = ...
1
vote
1answer
68 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
83 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 ...
0
votes
2answers
129 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 ...
0
votes
0answers
60 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 ...
4
votes
4answers
473 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 $(x_0, y_0, z_0)$?