Tagged Questions
0
votes
2answers
33 views
Ray-Lens Intersection
So imagine that I have a ray parameterized as $\vec{R} = \vec{O} + t\vec{D}$, where $\vec{O}$ = origin, $t$ = parameter and $\vec{D}$ = direction vector.
I also have a spherical lens with aperture ...
0
votes
1answer
14 views
Ray Disk intersection
So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
0
votes
1answer
30 views
Find position on surface of a lens
If I have a lens with coordinates UV on the lens surface where U, V are [-1, 1] and I want to find the real-world (x,y,z) coordinates of the UV point, how would I do that if I have the following ...
0
votes
1answer
24 views
How to check the visibility of these three points?
For question d part i, I have calculated the distances from $Q$ to $P_1$ and $P_2$ respectively and found $P_1$ to be closer with a distance of root $6$, with $P_2$ having a distance of root $24$.
...
0
votes
0answers
47 views
Torus equation in terms of tangent
So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and ...
0
votes
1answer
38 views
3D Surface parametrization basics
I'm studying 3D rendering: I have a surface and the points on the surface are given by some function f such that $p = f (u, v)$
Since I'm a newbie this is unclear to me: how can a function of u and v ...
0
votes
1answer
31 views
parabola in homogeneous coordinates
So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what?
The reason I ask is because I have a 3*3 matrix ...
2
votes
0answers
180 views
Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?
I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly.
I know
$$\nabla\times E= ...
1
vote
1answer
821 views
Equation for making a circle in 3D space
I have a 3D space with axis $(x, y ,z)$ and I can make a circle in the $xy$-plane.
To make a circle in the xy-plane I currently use spherical coordinates $(r, \theta, \phi)$ where $r = 1$, $\theta = ...
0
votes
2answers
116 views
A circle on the plane [duplicate]
Possible Duplicate:
Parametric Equation of a Circle in 3D Space?
I know that, for example, if a circle is on a plane with counter-clockwise orientation, and with center $(a,b)$ and radius ...
1
vote
0answers
94 views
Distance between point and a spiral
I'm trying to work out an algorithm where, given the equation for a spiral in polar coordinates, $r(\theta)$, and a point rectilinear coordinates, $P(x,y)$, I can work out the minimum distance between ...
0
votes
1answer
130 views
Is this valid parametric equation to create control points for a helix in 3D space?
Is this a valid way to compute new points that are on a helix and if not what is it wrong?
The Cartesian coordinates of each new helix control point could be described by the following ...
0
votes
0answers
438 views
Converting standard equation for a paraboloid to a parametric one
I have the equation for a hyperbolic paraboloid in $x$, $y$, and $z$:
$$\frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2}$$
I also have the parametric equations for the same parabaloid:
$$x = a u ...
2
votes
2answers
923 views
Derive parametric equations for sphere
How do you derive the parametric equations for a sphere?
\begin{align}
x & = r \cos(\theta)\sin(\varphi), \\
y & = r \sin(\theta)\sin(\varphi), \\
z & = r \cos(\varphi),
\end{align}
where ...
2
votes
0answers
388 views
Explain Triangle perimeter in polar coordinates
The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle. ...
2
votes
1answer
445 views
Equation for control point distance for fixed-length cubic Bézier path (with specific constraints)
A particular Stack Overflow question asks how to construct a specific cubic Bézier path of constant length. I have experimentally determined the ideal distances of the control points from the nearest ...
2
votes
1answer
106 views
Finding Angle of Elevation to hit X, Y
My ultimate goal is to find the angle of elevation necessary to launch a projectile from the origin to (x,y) with initial velocity V and under gravitational acceleration g. Wind resistance is ignored.
...
1
vote
2answers
275 views
Finding a quadratic Bézier curve of length $l$ between two points
I have two points $P_1$ and $P_2$ in the plane. For each of the points, I have two vectors $v_1$ and $v_2$. I want to find a quadratic Bézier curve from $P_1$ to $P_2$ of length $l$ leaving $P_1$ in ...
