1
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0answers
33 views

Intersection between 2 lines (3D). This doesn't have a solution does it?

so I was looking through an old exam and this question was given: The teachers answer was the point (9, -9, 21) I tried solving this myself, I got x = x, y = y, but I could not find a point where ...
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2answers
18 views

Parametric equation for intersection of curve

Here's the three part question: A) Find parametric equations for curve which is the intersection of the cylinder $x^2 + z^2 = 1$ and the plane y = -x. B) Show that the curve lies on the surface $x^2 ...
1
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2answers
61 views

Calculating Intersection of Three Spheres Step by Step

How do I calculate the intersection of three spheres step by step? Assume that the spheres are $S_i(c_i, r_i)$ where $i = 1,2,3$, $c_i$ is the center coordinates of $S_i$ and $r_i$ is the radius of ...
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1answer
154 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 ...
1
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1answer
42 views

Find intersection of 2 parameterized planes

I have two parameterized planes, for example, {u, 0, v} and {u-1, v-1, 1}. And I have to find the parametric equation of the line that intersects both planes. By setting both planes equal to each ...
1
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1answer
51 views

Find the intersection of two planes.

Find the intersection of the planes $x+(y-1)+z=0$ and $-x+(y+1)-z=0$. These two planes are 3-dimensional and I am confused on how to solve it.
2
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0answers
91 views

What is the Area formed when a line is traced between two 3D curves?

This question is quite related to intersection of cylinders, Hyperbolic paraboloid and modelling. I am welding a trunnion to a pipe (both are hollow cylinders in different geometry). They intersect ...
1
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1answer
60 views

Determine if a point is contained in the circle in 3d space

I have a problem where I need to determine if a point is contained in the area of a circle in 3d space. For my circle, I have the radius (R), the position of the center (C) and a normal vector to the ...
0
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0answers
85 views

Ray and Elliptic Paraboloid intersection

I have ray: P + V*t*. An elliptic paraboloid: focal point: r0 + f * n (orientation of the paraboloid is n from the point r0 with f distance) I would like to find the intersection(s) of the ...
2
votes
3answers
524 views

How to check if point is within a rectangle on a plane in 3d space

Please refer to this image for this question-> I have a 3d bounded box (in green). I also have a 3d line (in red) I know the points a, b, c, d, e. They are points in space with x, y, z, ...
2
votes
1answer
194 views

How do I find the outline resulting from the intersection of a NURBS surface and a plane?

The context for this question is 3D printing. Currently the way it's done is: Convert a 3D model to a mesh of triangles Ensure it's manifold and that there are no degenerate triangles 'Slice' this ...
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votes
0answers
100 views

Intersection of a hollow cone and a circular disc in 3D

I'm trying to calculate the area of a hollow cone intersecting a circular region on a surface. Basically a hollow cone is defined by its starting apex and its ending apex, the height of the cone from ...
1
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1answer
258 views

3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
0
votes
1answer
428 views

Intersection between sphere and cylinder

I have a sphere and a cylinder. I have the center and the radius of each of them. the sphere: radius = $r_1$ center = $(x_1,y_1,z_1)$ the cylinder: radius = $r_2$ height = $h_2$ center = ...
1
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0answers
84 views

Vector Tangent to Curve of Intersection

I am having problems solving this. Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$. I'm able to do this kind of thing using ...
1
vote
1answer
46 views

How many faces can have at most the intersection of two rectangular frustums?

In a 3D context, I want to evaluate the intersection of two rectangular frustums. The intersection of those two frustums will be a convex polytope, I think. What will be the maximum number of faces ...
1
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1answer
258 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
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1answer
527 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
0
votes
1answer
453 views

Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a bit more complicated than the post title suggests because I was running out of words. I suppose the full title would be: "Finding the distance between the centre of an arbitrarily rotated ...
2
votes
1answer
305 views

points of intersection on a randomly situated plane and ellipsoid (spherical) in 3d space

if i have an ellipsoid and a plane oriented in any way in a 3 dimensional coordinate system, and they intersect; is there a way to find an equation that describes (or at least approximates) all points ...
2
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1answer
185 views

How to determine the intersection of 6 planes?

ABCD is a tetrahedron (not necessarly a regular one). A Monge's plane is a plane which is perpendicular to an edge and goes through the middle of the opposite edge. I want to prove that the 6 ...
3
votes
1answer
511 views

Plane intersecting line segment

I have a plane which is represented as a 3d point $\vec{p}$ with a normal $\hat{n}$. I also have a line segment specified by two points $\vec{v_1},\vec{v_2}$ . I want to get the intersection point (if ...
3
votes
3answers
473 views

Three non-coplanar lines in the 3D-space always have a fourth one that intersect them all?

If I have three lines $a,$ $b$ and $c$ in the euclidean 3D space, which are pairwise non-coplanar, is there always a fourth line $x$, that intersects theses three lines?
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1answer
498 views

Intersection of spherical caps

Short version: if two spherical caps of the same sphere intersect, how can I determined the coordinates of the two "singular points" of this intersection Long version: On a unit sphere, centered at ...