Simulated here is a projectile path under gravity, assuming g = 9.8 m/s^2.

• A "side-view" 2-D plot of the path is created.
• The origin is at center of the plot, the +x-axis is to the right, and the +y-axis is up. Min and max values of x and y are hard coded.

Integer inputs:

• num_pts = number of points to plot along the path >=2
• theta_0_deg = launch angle in degrees measured from the +x-axis: -179 <= theta_0_deg <= +180 degrees
• v_0 = launch velocity magnitude: 1 <= v_0` (in units of m/s)

After input, theta_0_deg and v_0 are scaled up to be FP (fixed point) values, and theta_0_deg is also converted to radians, resulting in theta_0_fp and v_0_fp. The FP scale is SCALE_FP = 10**20.

projectile_plot.cairo contains:

• projectile_path- The view function which accepts user inputs and initiates all calculations
• position_fp_s_filler - The function which fills an array of x-coordinates and an array of y-coordinates

physics.cairo contains functions for physics calculations:

• time_in_plot_fp - Calculates the time that the projectile is in the plot area
• x_value_fp - Calculates the x-coordinate of the projectile at a given time
• y_value_fp - Calculates the y-coordinate of the projectile at a given time

math.cairo contains several math functions to use with fixed point quantities:

• Square root, multiplication, division
• Distance between two points
• cosine_6th_fp or cosine_8th_fp - Taylor series approximation of cosine (to 6th order, or to 8th order), requires -pi <= angle <= pi
• cos_approx_fp
  • Increases accuracy of Taylor series approximation of cosine (above) for angles in 2nd (theta_0_deg > 90) or 3rd (theta_0_deg < -90) quadrant, by (1) moving the angle to 1st or 4th quadrant (i.e. finding the mirror image of the angle, flipped across the y-axis), then (2) calling cosine_6th_fp or cosine_8th_fp, and then (3) forcing the cosine value to be negative (as it would be back in the 2nd or 3rd quadrant).
  • If theta_0_deg = 90 or -90, then it assigns the exact value, 0, to the cosine (rather than approximating).
• sin_approx_fp - Finds the sine of an angle, using a trig identity and the cosine of the angle.

constants.cairo contains:

• FP math constants
• Other math constants
• Physical parameters (except those that are user inputs)
• Plot parameters (except those that are user inputs)

test_projectile_plot.py

• Contains input parameters which are fed into both Cairo and Python calculations
• Contains other constants and parameters (that should match those in constants.cairo) for Python calculations
• Contains Python calculations of projectile path coordinates, to compare to same Cairo calculations done by calling projectile_path function from projectile_plot.cairo, using same input parameters
• Dumps calculated values to .json files (one each for cairo and python calculations) to be used by Jupyter notebook, test_projectile_plot.ipynb
• Prints for comparison the values (as FP) from the coordinate arrays found with Cairo and Python
• To run: pytest -s tests/test_projectile_plot.py

test_projectile_plot.ipynb

• Jupyter notebook which plots two projectile paths:
  • Array calculated in Cairo by projectile_plot.cairo
  • Array calculated in Python by test_projectile_plot.py
• Gets data from .json files created in test_projectile_plot.py
• To run:
  • Install Jupyter Notebook
  • jupyter notebook, follow instructions to open notebook in browser
  • Open file test_projectile_plot.ipynb

(An additional Jupyter notebook, prototype_projectile_plot.ipynb, was used to first prototype all calculations that were done in the Cairo files. The Python calculations here were then duplicated in test_projectile_plot.ipynb.)

Built with auditless/cairo-template

This repository is licensed under the MIT license.

The Cairo template currently supports building and testing contracts.

Build the contracts.

$ scarb build

Run the tests in src/test:

$ scarb run test

Format the Cairo source code (using Scarb):

$ scarb fmt

View the compiled Sierra output of your Cairo code:

$ scarb run sierra