Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.
0
votes
1answer
44 views
Triangle $z$-index interpolation between the vertices
I got a $2$D triangle, each vertex has a $2$D coordinate with a $z$-index value (NOT a $z$ coordinate!). The $z$-index value indicates whether a vertex lays on, in front of, or behind your screen ...
0
votes
2answers
31 views
computing the $y_{cm}$
Suppose I have a half disc and the coordinates axes at the centre of base of the disc. For the given system, I have surface mass density $S$ as $$S=S_0 sin\theta$$($S_0$ being positive constant). I ...
0
votes
2answers
50 views
Find the tangent to a function
Find the tangent to this
$\displaystyle y={1 \over x+3}$
it's crossing the point $(-2,1)$
I have drawn the lines but I can't calculate it
0
votes
1answer
59 views
How to handle two-center bipolar coordinates?
In my problem, I want to integrate a 2D function $f(x,y)$ which explicitly depends on the vector $ \vec{r}_1=\vec{r}-\vec{R}_1 $ and $\vec{r}_2=\vec{r}-\vec{R}_2$, where $\vec{R}_1=(a,0)$ and ...
0
votes
0answers
11 views
Converting DD to DMS and vice versa
I want to know how to convert DD(Decimal degrees) to DMS(degrees, minutes, seconds). I am creating a script that will convert DMS to DD. Please use 37.391933,-122.043667 decimal degree as an example ...
4
votes
1answer
99 views
Every conic in $\Bbb{P}^2$ equivalent to $XZ - Y^2$ - what is meant by hint here?
I am looking at Miles Reid's UAG book. There he claims that every projective conic is projectively equivalent to $XZ = Y^2$. He asks to show that $Q$ a non-degenerate quadratic form is such that ...
1
vote
1answer
29 views
Co-Ordinate Geometry : Please find the mistake
http://i.imgur.com/H59VgOK.png
I think there is some mistake in my diagram or the work. Please check the link .
The above formula is of Distance Formula(in the link). that is $$\sqrt{(x_2 - x_1)^2 ...
1
vote
0answers
25 views
Equation to calculate intersected cells in a grid, given a selection rectangle
I am looking for an equation which will calculate which cells (returned either as a pure index or as a row/col) are intersected by a selection rectangle when provided with the box coordinates of each ...
3
votes
0answers
58 views
How to solve a distance problem inside of a picture?
sorry for my bad english. I have the following problem:
In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y).
Now i want ...
0
votes
1answer
62 views
Find a locus of points to satisfy these conditions?
So, we have to straight lines:
$$3x-4y+5=0$$
$$2x+3y-4=0$$
You have to find a locus of points from which all perpendiculars to the two lines given are in a 2:3 ratio.
3
votes
2answers
51 views
Quick question regarding coordinate geometry
Note: My exam is in about 1 hour and i just realized that i have a unsolved paper, this is one of the questions that i wasn't able to answer from it. I would highly appreciate it if a full explanation ...
3
votes
3answers
64 views
Two questions for coordinate geometry
Note: I am burning through dozens of questions from sample papers and these i couldnt understand, these are not homework and i would appreciate it if the full answer could be provided.
The first ...
0
votes
0answers
28 views
Magnetometer electronics engineering " having values X,Y,Z How to calculate angle from north in 3d
Having values X,Y,Z Mathematics of How to calculate angle from north in 3d?
Thank's in advance
1
vote
0answers
24 views
Linear 2D transform in the sense of geometric figures?
Consider tranformation which turns one aligned rectangle to another:
This tranformation can be written in matrix form in the following way
where
...
0
votes
0answers
31 views
How to apply transformations to line equation?
I use line equation of style $y=a*x +b$ , I want to apply transformations (rotation, translation in $x$ and $y$) on the line without changing the form by only changing the $a$ and $b$, I know for ...
1
vote
1answer
113 views
triple integral - ecliptic coordinate
I need to find the $V$ by triple integral.
the limits from up is (1) - ecliptic cone.
and from dwon - (2) - elepsoide.
$$(1) \ \ \ \ z=-\sqrt{3x^2+5y^2}$$
$$(2) \ \ \ \ {3 \over 10}x^2+5y^2+{z^2 ...
0
votes
1answer
255 views
Angle between two coordinates(latitude, longitude) from a position on earth
Suppose I am standing at latitude, longitude $(-33, 151)$ and I want to calculate the angle between two points $(-32, 150)$ and $(-34, 152)$ from my point of view. Can someone please tell me how can I ...
2
votes
3answers
50 views
Find at least two ways to find $a, b$ and $c$ in the parabola equation
I've been fighting with this problem for some hours now, and i decided to ask the clever people on this website.
The parabola with the equation $y=ax^2+bx+c$ goes through the points $P, Q$ and $R$. ...
1
vote
1answer
61 views
Change of coordinate matrices
Find the change of coordinate matrices:
Wherein B is the standard basis for P2
$$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1)
$$
$$P_{B'B}$$ means the transformation for the ...
0
votes
1answer
83 views
Transformation of a matrix, change of basis
Find the change of coordinate matrices:
Wherein B is the standard basis for P2
$$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1)
$$
$$P_{B'B}$$ means the transformation for the ...
0
votes
1answer
132 views
get position of point given distance from other points?
I have a 2 points i know the distance between them with a 3rd points. how to get the position of the 3rd point given other distances with the other two points ?
2
votes
2answers
64 views
question on transformation
If a $2$d coordinate transformation function is given by $f(x,y)= 3x+1$, then what does it mean? How do I calculate the transformed coordinates for the points say $(3,4)$ in the initial space?
2
votes
1answer
56 views
A Question About Linear Interpolation
So lets say I have two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. $A$ and $B$ are each associated with some scalar value $K_1$ and $K_2$. $K_1$ is negative and $K_2$ is positive and all the ...
1
vote
1answer
48 views
Test of handedness
I'm reading a book on linear algebra, where the author gives a method to test the handedness or chirality of a given set of 3 basis vectors.
if (v1 x v2) . v3 > 0 then it's right-handed, while if ...
1
vote
2answers
98 views
Finding a coordinate vector for specific basis
I am having trouble with a specific problem concerning coordinate vectors. I have a basis $B' = \{t^2 + 2, t + 3, t^2 + t + 1\} $and a polynomial $p(t) = 4t^2 - t$. so I believed the way to go about ...
0
votes
0answers
23 views
Coordinate System in three dimensional system
I want to ask about the formula to find the height of an object with respect to the another object's position using the $x, y$ and $z$ coordinate system.
Like, I am making a game and it has terrain ...
3
votes
3answers
285 views
Tetrahedron problem (proving)
Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
0
votes
1answer
62 views
Reflecting a Point about a Line
I am looking for the abstract concept of rotating a point repeatedly.
Equilateral triangle ABC has vertices (0,0), (2,0), (1,$\sqrt{3}$).
If in an equilateral triangle ABC we take point X to be the ...
1
vote
2answers
85 views
Coordinate system conversion: what it is called what I'm doing?
I want to do a simple coordinate transformation and would like to know what is the rigorous way to describe this mathematically in order to be able to search for algorithms for more complex ...
0
votes
1answer
157 views
Find coordinates of equidistant points in Bezier curve
I have to find points (say 10 points) in Bezier curve with 2 control points such that they are at equidistant positions in the curve. Currently I am using the following formula which gives me points ...
1
vote
1answer
73 views
How to get Euler angles with respect to initial Euler angle
I have a sensor which gives me Euler angles (roll,pitch,yaw). There is a baseline value of Euler angle (assume it is $5,10,15$) at the beginning.I want to calibrate from this baseline values all ...
1
vote
2answers
30 views
find point on edge of rect between two points
If I have a rectangle { x = 25, y = 135, width = 30, height = 15 }, and a random point { x = 235, y = 320 }, how can I find the point along the edge of the rectangle that is between the center of the ...
0
votes
1answer
39 views
Determining direction based on (x,y) coordinates
I am making a $2D$ game where an enemy shoots a fireball at the player.
Both the player and the enemy have $(x, y)$ positions and are capable of facing in $8$ directions: UP, DOWN, LEFT, RIGHT, ...
0
votes
1answer
30 views
Burgers equation change of variable
In this paper on the Burgers equation (1.1),
$$ u_t = \left(\nu u_{xx} - \sigma u^2\right)_x, $$
the authors use a simple change of variables (2.1a,b)
$$\begin{align}
u(x,t) &= q(y,t) \\
x ...
1
vote
1answer
90 views
Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system
In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...
0
votes
1answer
25 views
Affects of a coordinate transformation
I am attempting to solve a PDE of $f(r,t)$, where $r\in[0,g(t)]$ is a spacial coordinate and $t$ is time. The PDE is coupled to to an ODE for $g(t)$.
I wish to simplify the problem by defining a new ...
0
votes
1answer
59 views
How to determine a Triangle vertices by its coordinates?
I have to solve this problem, yet I'm not sure what is asked.
Given a triangle whose vertices are defined by its coordinates. Determine where is the point O with the given coordinates - inside or ...
0
votes
1answer
97 views
transformation between square and a polygon?
I have a square and a polygon. I want to transform all the points inside this square such that they are mapped inside the polygon. I was trying using scale and rotate matrices but I am not able to ...
1
vote
1answer
44 views
Triangle and parametric coordinates
I'm studying on a book where it says: "A triangle is the set of points
where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
0
votes
1answer
46 views
How do I calculate a position in front of a quaternion given the initial position and the quaternion?
Well I want to determine the position in front of, lets say 'an object'.
'An objects' has a position (pX,pY,pZ) and a quaternion rotation (qX,qY,qZ,qW) (where qW seems always to be ...
0
votes
1answer
50 views
Zooming to an arbitary point [closed]
Maybe its a programming question, but im more interested the mathematical theory behind it.
I try to zoom to a given point (mouse cursor). just like google map. (here is the visualization: ...
2
votes
4answers
205 views
How do I determine if a point is within a rhombus?
I know the coordinates of the 4 rhombus' vertices. I also have the coordinates of another arbitrary point (the result of a click on the screen).
How do I determine if that point is within the ...
3
votes
4answers
338 views
Why do we draw the $xyz$ coordinate system like this?
Usually people (including, for instance, Calculus teachers) draw the $xyz$ coordinate system in such a way that the $y$ and $z$ axes are perpendicular to each other:
Imagine I actually got three ...
0
votes
1answer
36 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 ...
3
votes
1answer
72 views
Unusual function format and its partial derivatives.
I came across a function of this format:
$z = f(u,v)$ where $u = x^2y^2$ and $v = 5x + 1$
Because this function is not in the same format of the ones I've seen before (explicit or implicit), I don't ...
0
votes
2answers
50 views
Turning text-strings into (Cartesian) graphs
A friend told me of a neat site that could turn a text string into an equation for plotting that string, but he forgot to bookmark it.
Various web searches haven't helped (the more obvious terms like ...
0
votes
1answer
41 views
Find base from unit vector code - why changing sign?
I have the following code which accepts a v1 vector and outputs two other vectors to construct an orthonormal base
...
1
vote
1answer
64 views
Finding the rotation transform between coordinate frames in 3-Space given 1 point
I would like to find the rotation transform between two 3D Cartesian coordinate frames knowing only the magnitude and direction of a single vector shown in both frames. The vector passes through the ...
2
votes
3answers
157 views
The area of the triangle with vertices (3, 2), (3, 8), and (x, y) is 24. What is x?
The area of the triangle with vertices (3, 2), (3, 8), and (x, y) is 24. A possible value for x is: a) 7 b) 9 c) 11 d) 13 e) 15
Please show your work and explain.
0
votes
3answers
52 views
Doubt on subspace of a vector space
I am new to linear algebra and I have a doubt that : in 2D coordinate system is a line which is at 45 degree NOT passing through the origin a subspace of the vector space comprising the whole 2D plane ...
