Using Mathematica, we created a 3D representation of a soccer field including goals and a ball with our understanding of planes and spherical coordinates. The idea for our project came from Virginia running an intramural soccer club on campus and the similarities we found between the shapes we modeled in Lab 3 when learning about Polar, Cylindrical, and Spherical Coordinates as well as our understanding of planes to make the shapes of a soccer field.
In “Plot3D”, we used our understanding of the equa2on for planes, Z=zo+m(x-xo)+n(y- yo), and spherical coordinates with (ρ, φ, θ) and ρ = 1, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2 π. ρ = 1 to create a sphere with radius of 1. These were used to depict a planar field parallel to the xy-axis and a soccer ball. In “Plot3D” we depicted a plane with the equation z=0 since the values of m and n were 0. We used “Graphics 3D” to plot the coordinates of the vertices of each different plane and shape. These were then combined to create the whole soccer field. The ball made in “Plot 3D,” used the equation of a sphere with radius 1: f(x, y, z)=x^2 + y^2 + z^2 = 1^2 and we then used spherical coordinates where x = ρ sin(φ) cos(θ) y = ρ sin(φ) sin(θ) z = ρ cos(φ). Using spherical coordinates (ρ, φ, θ), we created the sphere by stating that ρ = 1, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2 π.
