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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3answers
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Find the Range and Domain of the following function

The function is: $f(x,y) = \frac{2}{\sqrt{3-x}} + \frac{1}{\sqrt{4-y}}$ I have found the domain and the Range intuitively. But how would I formally prove that my assumption of the Range and Domain ...
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1answer
28 views

How do you determine if two triangles are intersecting for collision detection?

I've been scouring the internet for things about intersecting triangles. I haven't been able to find something that just gives me the math and what all the variables are equal to. I would love the ...
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1answer
14 views

distances measured in space

how do we find the distance of a point from a given line measured parallel to a given plane? Here is a a sample question : find a distance of point (2, 3, 4) from line (x+3)/3=(y-2)/6=z/2 measured ...
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1answer
50 views

Change angle of a vector to another vector

Let $\mathbf{x},\mathbf{y},\mathbf{w}$ be the following 3-vectors: $$\mathbf{x}=\begin{pmatrix}x_{1}\\ x_{2}\\ x_{3}\end{pmatrix}\qquad\mathbf{y}=\begin{pmatrix}y_{1}\\ y_{2}\\ ...
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2answers
92 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 ...
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2answers
72 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
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2answers
75 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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1answer
18 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 ...
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0answers
59 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 ...
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1answer
207 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
57 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 ...
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1answer
34 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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2answers
20 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 ...
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2answers
17 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 ...
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3answers
43 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 = ...
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0answers
55 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 ...
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1answer
40 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
43 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 ...
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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 ...
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1answer
241 views

What is the line of greatest slope on a plane? [closed]

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 ...
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0answers
54 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. ...
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0answers
16 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 ...
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2answers
60 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 ...
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2answers
43 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?
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1answer
37 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 ...
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1answer
142 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: ...
2
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1answer
244 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 ...
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1answer
44 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 ...
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0answers
33 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 ...
3
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0answers
99 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 ...
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1answer
118 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 ...
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1answer
56 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 ...
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1answer
51 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 ...
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0answers
22 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 ...
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1answer
44 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 ...
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1answer
91 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 ...
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2answers
49 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
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2answers
124 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
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3answers
350 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 ...
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1answer
83 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 ...
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1answer
76 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 ...
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1answer
25 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 ...
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2answers
142 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 ...
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3answers
219 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 ...
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0answers
24 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 ...
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1answer
17 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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1answer
39 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?
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1answer
37 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 ...
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3answers
49 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 ...
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2answers
50 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 ...