I'm intersecting a line in 2D and I calculate the X,Y coordinates of the intersection point. What I need is the Z of the intersection point given the X,Y,Z of the line points, and the X,Y of the intersection. From what I understand of equations it should be a one-liner but I don't know enough math to get there.
Your question is rather vague, but I will try to answer.
So take following equation:
Let's note it as Fx(X) = Fy(Y) = Fz(Z) and take a part of it:
Fx(X) = Fz(Z)
Then you said you know x, y and z for two points, put it to x1, x2, z1, z2 accordingly. Then put x of intersection to x. Now you have a linear equation with one variable z. Here it is:
z = (x - x1) / (x2 - x1) * (z2 - z1) + z1
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Find coordinates to draw arrow head (isoscele triangle) at the end of a line
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I have drawn a line (x1, y1), (x2, y2) and would now like to draw 2 more lines that would form an arrowhead at point (x2, y2). How do I determine the 2 points to which I need to draw the arrowheads from point (x2, y2)? I know that I need to find 2 points on a circle with center at point (x2, y2) that are equidistant from line (x1, y1), (x2, y2) but I do not know how to find this. Geometry is not my forte.
Your line is vector from (x1,y1) to (x2,y2), its components are
D = (dx, dy) = (x2-x1, y2-y1)
Length of vector (perhaps you have Hypot function in math library):
Norm = Sqrt(dx * dx + dy * dy)
Normalized (unit length) vector:
uD = (udx, udy) = (dx/Norm, dy/Norm)
(again - math library might contain a function for normalized vector to replace two last formulas)
Unit perpendicular vector:
uP = (upx, upy) = (-udy, udx)
Now make two points at distance L along line from line end, and with perpendicular distance W from the line:
ax = x2 - udx * L + W * upx
ay = y2 - udy * L + W * upy
bx = x2 - udx * L - W * upx
by = y2 - udy * L - W * upy
At last draw lines A-P2 and B-P2
P.S. If you want to define arrow angle, tg(alpha) = W/L, also you can look at calculations here
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I tried to do my homework and i'm not sure if I did it right. I'm not entirely sure how linspace works and was hoping for some input on my code! I'll attach the assignment it's based on. [enter link description here][1]
[enter image description here][2]
clc
clear all
figure(1);
figure(1);
x = 0:0.1:10
y1 = exp(-0.5*x).*sin(2*x)
y2 = exp(-0.5*x).*cos(2*x)
plot(x,y1,'-b',x,y2,'--r')
legend('y1','y2');
grid on
xlabel('\bfx axis');
ylabel('\bfy axis');
title('Sin and Cos Functions')
figure(2);
subplot(2,2,1)
plot(x,y1,'-b');
legend('y1','Location','northeast');
grid on
xlabel('\bfx')
ylabel('\bfy1')
title('Subplot of x and y1')
figure(3)
subplot(2,2,2)
plot(x,y2,'--r');
legend('y2','Location','northeast');
grid on
xlabel('\bfx')
ylabel('\bfy2')
title('Subplot of x and y2')
figure(4)
x = linspace(-2,8,200);
fun=(x.^2-6*x+5)./(x-3)
plot(x,fun,'b-','LineWidth',2)
axis([-2 8 -10 10]);
hold on;
title('Plot of f(x)')
xlabel('\bfx')
ylabel('\bfy')
(50 Points) Plot the function y(x) = (e^-0.5x)(Sin2x) for 100 values of x between 0 and 10. Use solid blue line for this function. Then plot the function y(x) = (e^-0.5x)(Cos2x)on the same axis. Use dashed red line for this function. Be sure to include a legend, title, axis labels and grid on the plots. Re-graph the two functions using subplot.
(50 Points) Plot the function Plot the function f(x)= ((X^2)-6x-5)/(x-3) using 200 points over the range −2 ≤ x ≤ 8. Note that there is an asymptote at x = 3, so the function will tent to infinity near to that point. In order to see the rest of the plot properly, you will need to limit the y-axis to the range -10 to 10.
linspace takes 3 arguments: a starting value, an ending value, and n = the number of points you want to generate in between those two numbers. It outputs an array of n evenly spaced numbers between your starting and ending values. For example linspace(0, 10, 5) returns an array of 5 evenly spaced numbers starting with 0 and ending with 10.
Here's the code for figure 1
x = linspace(0, 10, 100);
y1 = exp(-0.5*x).*sin(2*x);
y2 = exp(-0.5*x).*cos(2*x);
figure(1)
plot(x, y1, '-b', x, y2, '--r')
title('This is the title')
legend('This is Y1', 'This is Y2')
xlabel('These are the X values')
ylabel('These are the Y values')
grid on
Figure 2. Both subplots can be under one figure handle (i.e. figure(2)).
figure(2)
subplot(2, 1, 1)
plot(x, y1, '-b')
title('This is the first subplot')
xlabel('X axis')
ylabel('Y axis')
grid on
subplot(2, 1, 2)
plot(x, y2, '--r')
title('This is the second subplot')
xlabel('Another X axis')
ylabel('Another Y axis')
grid on
Figure 3. Your code looks right. Here's a similar solution:
x2 = linspace(-2, 8, 200);
y3 = ((x2.^2)-6.*x2-5)./(x2-3);
figure(3)
plot(x2, y3, '-g')
title('The third figure')
grid on
ylim([-10 10])
xlabel('Another axis')
ylabel('The last axis')
I have an m by n rectangular grid with c possible colors for each gridpoint. I want to use OR-Tools to find a valid coloring. What is the best way to do it?
I was thinking that it might be adding an OnlyEnforceIf clause for each pair of columns per row (based on color assignment equality), and then asserting that if an aligned pair in two different rows are also equal, then the two pairs cannot have the same color.
However, this seems very verbose, and introduces a lot of new variables.
Just create
color[x, y, c] a boolean var that is true of point (x, y) has color c.
then add the constraints:
Each point has exactly one color
for each (x, y):
sum over c color[x, y, c] == 1
Any rectangle is not uni color:
for each x1, y1, x2, y2, c: # (x2 > x1, y2 > y1)
BoolOr(color[x1, y1, c].Not(),
color[x1, y2, c].Not(),
color[x2, y1, c].Not(),
color[x2, y2, c].Not())
I have 3d data that makes a surface when plotted in 3d:
x1 y1 f(x1, y1)
x1 y2 f(x1, y2)
.. .. ..
x1 yn f(x1, yn)
x2 y1 f(x1, y1)
x2 y2 f(x1, y2)
.. .. ..
x2 yn f(x1, yn)
.
.
I can use gnuplot to get level curve for x=constant by using :
plot "datafile.txt" u 2:3 index 0 //or index 1 etc
How can I get plot for y=constant ?
Thanks for reply in advance...
1st possibility: plot the whole file, and make all unwanted datapoints invalid (NaN or 1/0)
yfix = 5 # the constant y value
plot datafile using (($2 == yfix) ? $1 : NaN):3
2nd possibility: the every specifier
n = 3 # number of the wanted sample in y-direction
plot datafile every ::n::n using 1:3
It takes as option (line increment):(block increment):(first line):(first block):(last line):(last block)
So the command above plots only the n'th line from each block, resp. dataset.
(note: blocks are separated by a single blank line, datasets by an additional second blank line. The latter are specified with index, the former addressed via every)
I have a game represented like this :
I would like to calculate the coordinates of the point x4,y4.
What I know is :
y4 = y3, x4 is on the line x1,y1,x2,y2 and the line is 45° (degree)
I tried x4 = y4 - y1 + x1 but it doesn't work very well..
Any ideas ?
m= (y2-y1)/(x2-x1) = (y4-y1)/(x4-x1)=1 as slope is 45 degree.
so x4=x1+y4-y1;
substitute y4=y3;
then X4 = x1+y3-y1;
This video should help you to get the right formula.
Should be:
m = (y2 - y1) / (x2 - x1)
b = y2 - m * x2
x4 = (y3 - b) / m
Since the line is at a 45° angle, dx=dy between two points on the line. Thus:
x4 = x1+(y1-y4)