Plotting

Don’t use loops, unless the opposite is explicitly stated.

  1. task1 Plot the function \(\sin(x) + \sin(3x)\) from \(-2\pi\) to \(2\pi\). The function task1 should both create a plot, and return two values: x and y with coordintes of points that were passed to plot(x,y).
  2. task2 Plot \(\sin(x) + \frac1{2}\sin(2x) + \frac1{3}\sin(3x) + \cdots + \frac1{10}\sin(10x)\). Think how to do it without loops. Remember, that sin accepts matrices and evaluates results for each element separately. Return the result the same way you did in the previous task.
  3. taskA You are given a matrix A of the size \(N\times2\), each row contains coordinates of one point on the plane. In this task the function should not return results, and it should only draw one picture consisting of the following:
    1. Draw set A
    2. Draw the center of mass for A.
    3. Create and draw the set B that is a translation of A in such a way that its center of mass is in \((0, 0)\). Remind: translated by the vector \((dx, dy)\), point \((x, y)\) goes to \((x + dx, y + dy)\).
    4. Create and draw the set C: a rotation of A around (0, 0) by \(5^\circ\). Remind: to rotate the point \((x, y)\) by \(\varphi\) around zero, one should left-multiply \(\begin{pmatrix}x\\y\end{pmatrix}\) by the matrix \(\begin{pmatrix}\cos(\varphi)&\sin(\varphi)\\-\sin(\varphi)&\cos(\varphi)\end{pmatrix}\).
    5. Create and draw the set D: A rotation of А around its center of mass by \(5^\circ\).

    Draw each set with a different color and a different marker.

  4. task10circles Draw 10 concentric circles with radiuses: 1, 2, …, 10. Use the fact, that points with coordinates \((\cos(\varphi), \sin(\varphi))\) lay on a circle of radius 1, when \(\varphi\) changes from 0 to \(2\pi\).

  5. plot_line You are given a linear matrix [a, b, c]. You are also given matrices xrange=[xmin, xmax] and yrange=[ymin, ymax]. Plot a line \(ax + by + c = 0\), and draw only that part of the line, that is contained inside a rectangle \(x_{min} \leq x \leq x_{max}\), and \(y_{min} \leq y \leq y_{max}\). Consider all the cases, including vertical lines.

    One of the ways to solve the task is as follows: intersect the line with each of the rectangle sides. They are horizontal and vertical, so it is quite easy to find intersections. Usually, you are left with only two intersections, so you now can call plot() for the line between the two points.

  6. plot_lines. You are given a matrix a with lines (the same as matrices from the block octave-vectorization, you are also given xrange, yrange with ranges to draw the lines by means of the plot_line function from the previous task. Draw all of the lines from a. Use a loop to call plotting for each line.
  7. plot_lines_and_intersections You are given the same as in the previous task. Draw all lines from the matrix a and draw all the intersections. Remember, that you have already implemented evaluating of intersections in the block octave-vectorization.