Questions tagged [3d]

For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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Great Circles and Inscribed Cube

A cube is inscribed within a sphere. How many distinct great circles are there that contain at least 2 vertices of the cube along its perimeter? Intuition tells me any great circle that coincides with ...
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Gradient of a function on a unit sphere in rotated coordinates

I have a function $f(\theta,\phi)$, where $(\theta,\phi)$ are spherical coordinates with $\theta$ measured from the positive $z$ axis. I also have the gradient $\nabla f = (\frac{\partial f}{\partial\...
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Optimization : Solve $4$ unknowns using $4$ equations

Suppose we have 4 points say A($x_1,y_1,z_1$), B($x_2,y_2,z_2$),C($x_3,y_3,z_3$), D($x_4,y_4,z_4$). Where $x_1,x_2,x_3,x_4,y_1,y_2,y_3,y_4$ are known points and rest $z_1,z_2,z_3,z_4$ are unknown ...
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Limits of SVD technique into fitting 3d plane

I'm asking what happens if I try to fit a plane against a particular 3d point cloud when points are collinear and I'm using the SVD technique. I read many posts explaining the technique with a generic ...
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Rendering a 2D image of a 3D rectangular cuboid

I'm trying to make a 2D map from data used to build a 3D scene. No perspective, just a flat view. An arbitrary series of transforms are applied to shapes, so they can be translated/rotated/scaled on ...
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If the mirror image of $P(a,6,9)$ with respect to line $\frac{x-3}{7} =\frac{y-2}{5}=\frac{z-1}{-9}$..

If the mirror image of $P(a,6,9)$ with respect to line $\frac{x-3}{7} =\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20,b,-a-9)$, then find $|a+b|$ The general point of the line is $(3+7k,2+5k,1-9k)$ The ...
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Find the parametrization of the intersection of two surfaces

I need to find the parametrization of the intersection for the two surfaces defined by these equations: $x^2+y^2=25$ and $z^2+y^2=25$ I'm not quite sure how to do it. What is the best way?
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The dot product in the room (third dimension) equal to the axies-values of the two vectors. [duplicate]

Why is it that the dot product of two vectors $u_1=(a, b, c)$ and $u_2=(x, y, z)$ plays out like this: $u_1 \cdot u_2 = ax+by+cz$. I have seen and understand why this is the case for 2D but why is it ...
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Given a 2D polygon in 3D space identify all points that are not a part of the polygon

I do not have a background in mathematics. I am a developer attempting to process point cloud data, but I believe this to be the correct place to post for this type of problem. Given points of a ...
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Converting a 3D point (x,y,z) into a 2D point (x,y)

I am currently trying to export out a series of points (x,y,z) that my software has identified on a 3D model into a report. The thing is, I would also like to impose these 3-dimensional points onto a ...
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Surface represented by the equation $x^2-2y^2+3z^2+5yz-6xz-4xy+8x-19y-2z-20=0$

I have the following second degree equation in $x,y$ & $z$: $x^2-2y^2+3z^2+5yz-6xz-4xy+8x-19y-2z-20=0$ I calculated the discriminating cubic as: $k^3-4k^2-97k-190=0$ The roots of this equation are ...
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Cross product, but with angles

I have two unit-length vectors $\vec{v_1}$ and $\vec{v_2}$ and I would like to find a unit-length vector that's perpendicular to them, so basically $\vec{v_3} = \vec{v_1} \times \vec{v_2}$. However ...
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Recurrence relation for the volume of a series of truncated cones

I'm struggling to find the recurrence relation to evaluate the volume of a solid formed by a series of truncated cones one on top of the other. The image below illustrates the problem for 2 truncated ...
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My question is about a shape I don't know but have an idea, tell me which shape is it? [closed]

So this shape is like a sphere but in place of circles put squares with sides changing in length? What would it look like also if the radius changes at different rate with distance then tell its ...
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There is a rectangle in 3-dimensional space. If I am only given the $x$ and $y$ coordinates, how do I find the $z$ coordinates? [closed]

We are given the $x$ and $y$ coordinates of the four vertices of a rectangle. How do I find the $z$-coordinates? I know that this 3 dimensional rectangle must obey all the usual conditions of ...
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How do I prove that a line is perpendicular to a plane given their conditions? How can I extract a vector out of the line condition?

Given the condition of a line $l:-x=z-1 \land y=1$, and the condition of a plane $\alpha:x-z=0$, how can I prove that $l\perp\alpha$? I know that the vector normal to $\alpha$, will be parallel to the ...
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Whats the volume of parallelopiped with two of its sides eqal?

If the volume of a parallelopiped of sides $\vec{a},\vec{b},\vec{c}$ is given by $$\det\begin{pmatrix}\vec{a} & \vec{b} &\vec{c}\end{pmatrix}$$ But if two of those vectors are equal then $\det\...
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What is the best allround mathematical software? [closed]

I know the big names such as MATLAB, Mathematica, and Maple. But they are all too expensive for me. I need a software with curve-fitting, 3D Graphs, and all other standard data visualization tools. ...
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Showing an organised top down view of a 3D function with Maxima

I'm trying to use Maxima to show the top down view of a 3D function, the different values (height/depth) of the function will be shown using a range of colours and a colour bar that Maxima provides ...
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1answer
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Simplifying Complex Propagation Constant of an Electromagnetic Plane Wave

I am attempting to study for an exam and encountered a problem involving an electromagnetic plane wave with a provided electric field and propagation constant, but despite setting up the solution ...
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How to calculate 3D position and update it

I'm trying to calculate the new position of an object moving over the surface of a 3D sphere after some time Δt, from X1 to X2 always onto the surface of the sphere. The measurements/data I have of ...
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Mathematics behind simultaneous 3d rotations

I'm trying to simulate the effect of two simultaneous rotations acting on a sphere, more specifically: rotation and precession of the earth. These two rotations act on different rates and different ...
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1answer
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Show that the curve is contained in a plane.

If all osculating planes of a regular curve pass through one point, show that the curve is contained in a plane. The osculating plane equation is as follows: $$\begin{vmatrix} X-x & Y-y & Z-z ...
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How to calculate this angle from 2 points in 3d space?

How do I find the following angle $a$ given $2$ points $(x, y, z)$ in $3$-dimensional space? I've drawn $2$ points, one in green, one in red. The curved black line being the earth, and the normal ...
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finding the shape of the higher order equations

Is there any way to find the shape of the higher-order equation like this one? I am more interested in making an initial guess about the shape (fast prediction) and then the process to find it. Any ...
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Position and Rotation of object with 4 Points (perspective view)

I am so confused about this. I found many links for example this one: link What I have: A perspective view with fixed position An object with 4 points (Green) and a point (Red) like these: I know ...
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Arrange a point relative to another within 3D space

According to this accepted answer on Stack Overflow, you ... need to set the coordinates m41, m42 and m43 of an SCNMatrix4 B (representing the last column and the first three rows of a 4x4 matrix) to ...
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How to compute the multivariable limit of a multivariable function as the variables approach infinity.

Consider a particle in a three-dimensional potential $$V(x,y,z)=\frac{A \left(x^3+2 y^3+3 z^3+4 a^3\right)}{\left(x^2+y^2+z^2+a^2\right)^2}$$ This particle has scattering states if $E>E_0$, where $...
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Find the plane containing line $\frac{x-3}{2} = \frac{y+2}{2} =\frac{z-1}{3}$ and also contains its projection on the plane $2x+3y-z=5$

I am not really able to understand the question. I didn’t get the part ‘contains the projection of the line on the plane....’ How can a plane contain the projection of a line on another plane? Wouldn’...
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The length of projection of the line segment joining the points $(1, –1, 0)$ and $(–1, 0, 1)$ to the plane $2x + y + 6z = 1$ is equal to?

The length of projection of the line segment joining the points $(1, –1, 0)$ and $(–1, 0, 1)$ to the plane $2x + y + 6z = 1$ is equal to? I am confused if i have to find the length of perpendicular ...
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0answers
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Confusing result in calculating normals

I am working on a 3D graphics engine and one thing that is important is defining a "front" face and a "back" face of triangles that I define. A convention is, that the vertices of ...
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1answer
57 views

Lines $\frac{x−x_0}{a_1}=\frac{y−y_0}{a_2}=\frac{z−z_0}{a_3}$ and $\frac{x−x_0}{b_1}=\frac{y−y_0}{b_2}=\frac{z−z_0}{b_3}$ if $a_1b_1+a_2b_2+a_3b_3=0$

I think this is a really interesting question. I think that we could create a system of equation that would prove that the two lines are parallel but I am not entirely sure. Anyone knows how to tackle ...
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Where does the line $(x − x_{0})/a_{1} = (y − y_{0})/a_{2} = (z − z_{0})/a_{3}$ intersect the $xy$-plane? [closed]

I guess the $z$ part should be equal to $0$ or something of the sort but I am having some trouble with this question.
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Coordinates of longitude and latitude in 3d.

The Earth is centered at the origin of a 3d graph, such that the xy-plane has the equator, the xz-plane has the prime meridian, and the north pole is on the positive z-axis. Find the Cartesian ...
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3answers
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Vectors in 3D and area of a triangle

I have three points with coordinates: $A (5,-1,0),B(2,4,10)$, and $C(6,-1,4)$. I have the following vectors $\overrightarrow {CA} = (-1, 0, -4)$ and $\overrightarrow{CB} = (-4, 5, 6)$. To find the ...
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1answer
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A question about 3D Trigonometry [closed]

The questions I am stumped on are parts c) and d). I am bewildered as to which triangles I am meant to use. For context, I have got an answer of 54.7 for part b and this is correct. Solutions to c and ...
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Finding the closest triangle matching the inverse uv mapping

I have an algorithm which takes 2 triangles ABC and PMN, where ABC is the triangle that is rendered and PMN is an extra triangle that is used for texture mapping and converts the PMN triangle to UV, ...
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1answer
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how to rotate a vector in 3d space around arbitrary axis

In my case I have two arbitrary vectors (suppose vector AB and CD ) and I am assuming that some rotation operation will happen to vector AB to get it the orientation of vector CD. so by using the ...
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Prove that among 9 points in regular tetrahedron of side 2, two are no more distant than 1

I've stumbled onto a problem. I need to prove that among any 9 points chosen from a regular tetrahedron of side equal to 2, there always are two such that the distance between the two is not greater ...
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1answer
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Recalculating a point onto a custom plane

This is my coordinate system: ______ Essentially, I want to know if it's possible to recalculate a point 'A' from 1 plane (ZY plane) onto another plane (B plane) more efficiently than the way I'm ...
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1answer
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Cross section of a plane in a cube

A plane is going through a cube so the cross section is a pentagon. Prove that the area of the pentagon is smaller than the product of the pentagon's two largest sides. The first thing I tried to do ...
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1answer
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Mapping from a perspective projected square to the original one

A square viewed from an angle becomes an isosceles trapezoid. Assuming we are looking at the middle of the square, if we know everything about this trapezoid, how to map every coordinate on it to the ...
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Calculating pose in terms of Euler angles for a plane using direction vectors.

I'm trying to find the pose of a rectangular plane in 3D space. I have two orthogonal vectors $\vec{a}$ and $\vec{b}$ that lie on the plane and centered at the origin. I take the cross product of the ...
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1answer
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Maximizing angle between three unit vectors

Find the maximum angle between three equally inclined unit vectors in the 3D space. My attempt Define unit vectors $\hat{a},\hat{b},\hat{c}$ and their components $a_i,b_i,c_i, i\in \{1,2,3\}$ Note ...
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A question about quaternion [closed]

I am an 8 grade student.Who can tell me what is quaternion???Please use SIMPLE and understandable words(I am a Chinese)
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How can I calculate distance from two pixels HSV?

I want to look for a better way to calculate the distance between two pixels in the HSV color space. In my program I used Euclidean distance. $$ distance(p_1, p_2) = \sqrt{(h_1 - h_2)^2 + (s_1 - s_2)^...
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Angle of reflection on 3d Object

I am rasterizing some 3d objects (x,y,z) onto a 2d plane (x,y) and I want to color the rasterized cells based on the angle of reflection of an angle of incidence that comes from directly above the ...
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Formula for volume of a tetrahedron

Is there any formula for the volume of a tetrahedron in terms of the areas of its four faces ? Need any assumptions be necessarily made ( like each face altitude, circum-radius) etc? EDIT Like to know....
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2answers
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What formulas are required to calculate a 3d transformation?

Considering the point of view of square A and B, what math tranformations must be applied (either to the 3d camera or world) to transition from A to B? I can tell that for the B viewpoint I had to ...
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1answer
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Looking for a sort of an impulse function in 3D

I honestly don't know how I could've phrased this any differently (I feel like it's an impulse function because it's non-zero at only one point), but here it goes. I want a function that is non-zero ...

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