2
votes
1answer
26 views

Projective and affine conic classification

I have a doubt on the classification of non-degenerate conics (parabola, ellipse, hyperbola) in projective geometry (my textbook is "Multiple View Geometry in Computer Vision", which, as the title ...
0
votes
1answer
54 views

How to determine if two ellipse have at least one intersection point

All of the question are in sequence and related. 1.Given 2 ellipse with the position x1,y1, x2,y2 and the radius a1,b1, a2,b2, construct an equation to determine if both of them has at least one ...
0
votes
2answers
55 views

Find normal to ellipse through arbitrary points

I want to find the normal to ellipse through an arbitrary point. There is an array of points located arround a given ellipse (but not on ellipse curve). What I want to find is the normal of each of ...
0
votes
1answer
71 views

Find intersections of two ellipses who share one fixed point

Given two ellipses $e_1$ and $e_2$ with $$ e_1 = \{x: \lVert{x - F_1}\rVert + \lVert{x - F_2}\rVert = R \} $$ $$ e_2 = \{ x : \lVert{x - F_1}\rVert + \lVert{x - F_3}\rVert = R \} $$ where $F_1$ is ...
1
vote
2answers
38 views

Parabola and line proof

Given are three non-zero numbers $a, b, c \in \mathbb{R}$. The parabola with equation $y=ax^2+bx+c$ lies above the line with equation $y=cx$. Prove that the parabola with equation $y=cx^2-bx+a$ lies ...
1
vote
1answer
35 views

Disjoint conic sections?

is there any simple way to figure out whether two conic sections (e.g. two ellipses or an ellipse and a hyperbola) are disjoint or intersect each other? The conic sections are expected to be known ...
1
vote
0answers
78 views

Intersection between sphere and ellipsoid

I am failing since two days to compute and to plot the intersection of an ellipsoid in parametric notation ...
0
votes
0answers
90 views

Conic equation from cone/plane intersection

In an orthonormal cartesian frame $(O; \vec{x}, \vec{y}, \vec{z})$ consider: an infinite plane $P$ defined by: a point $p = (p_x, p_y, pz)$ an normal vector $\vec{n} = (n_x, n_y, n_z)$ a cone $C$ ...
0
votes
0answers
108 views

Find points of intersection with cone on a plane at a given angles

The provided variables are the cone angle(cA) of a cone that starts at the origin along the Z axis, the vertical angle (vA) of the direction the cone is facing, and a horizontal angle (hA) along with ...
1
vote
3answers
123 views

How to find the point on a parabola where x and y are equal?

On a parabola how could i find the point at which the y and x points are equal and meet on a point of the graph, algebraically?
3
votes
2answers
298 views

2D point projection on an ellipse

I would like to find an equation to this problem: The problem is that I have an ellipse at a given center point C, with radius a (x axis), and radius b (y-axis). So far so good. Now I have the ...
18
votes
0answers
459 views

How many points of intersection between an ellipse and an $L_p$-circle?

Consider an ellipse $E$ in the plane, centered at the origin. (In my case, the minor axis points into the nonnegative quadrant.) Let S be an "$L_p$-circle": $S = \{(x,y) : |x|^p + |y|^p = 1\}$, ...
2
votes
1answer
213 views

proof that intersection of two conic sections will intersect at at least two points.

In the following equation $\rho(x,y)$ returns a constant value for a given coordinate. $\mathbf n$ is the normal vector to the surface of the form $[P,Q,-1]$ and $s$ is a direction vector. ...
0
votes
1answer
1k views

Find the intersection of a line (segment) and an ellipse (from the center of ellipse)

Here is what I know: The location of the center of the ellipse C (20,10). The Major axis (2a) or 400 (a being 200) - this is on the X axis. The Minor axis (2b) or 200 (b being 100) - on the y axis. ...
2
votes
1answer
593 views

Find intersection(s) between parametrized parabola and a line

I'm trying to find the value(s) of the parameter $t$ at the intersection point(s) between a 2D general parabola (as a parametric function of $t$) and a line whose equations can be derived from two ...
0
votes
0answers
378 views

How to find intersections of hyperbolas by MATLAB

Let's have two hyperbolas given by equations: $$\mathbf{r}^T\cdot \mathbf A_1\cdot\mathbf r+\mathbf b_1^T\cdot\mathbf r+c_1=0$$ $$\mathbf{r}^T\cdot \mathbf A_2\cdot\mathbf r+\mathbf b_2^T\cdot\mathbf ...