Space Curvess

Praametric Curve Example 1

library(plot3D)

t_vals <- seq(0, 2, length.out = 100)

x_coords <- 2 * t_vals
y_coords <- 3 * t_vals^2
z_coords <- 4 * t_vals^3

scatter3D(x_coords, y_coords, z_coords, col = "blue")

Parametric Curve Example 2

library(plot3D)

t_range <- seq(0, 2*pi, length.out = 100)

x_points <- cos(t_range) + sin(t_range)^2
y_points <- sin(t_range) * (1 - cos(t_range))
z_points <- cos(t_range)

scatter3D(x_points, y_points, z_points, col = "green")

3D Surfaces

Planar Surface

library(plot3Drgl)

par(mai = c(1, 1, 0, 0))

x_axis <- seq(0, 4, length = 100)
y_axis <- seq(0, 2, length = 100)

plane_func <- function(x, y) (4 - x - 2*y) / 3
z_values <- outer(x_axis, y_axis, plane_func)

persp3Drgl(z = z_values, ticktype = "detailed")
planes3d(0, 0, 1, 0, col = "lightgray")

Saddle Surface

library(plot3Drgl)

par(mai = c(0.8, 0.8, 0, 0))

x_range <- seq(-4, 4, length = 100)
y_range <- seq(-3, 3, length = 100)

saddle <- function(x, y) x^2/16 - y^2/9
z_surface <- outer(x_range, y_range, saddle)

persp3Drgl(z = z_surface, ticktype = "detailed")

Spherical Surface

library(plot3Drgl)

mesh_grid = mesh(
  phi = seq(0, 2*pi, length.out = 100),
  theta = seq(0, pi, length.out = 100)
)

phi_vals = mesh_grid$phi
theta_vals = mesh_grid$theta
radius = 2

x_sphere = radius * sin(theta_vals) * cos(phi_vals)
y_sphere = radius * sin(theta_vals) * sin(phi_vals)
z_sphere = radius * cos(theta_vals)

surf3D(x_sphere, y_sphere, z_sphere, colvar = z_sphere)

Intersecting Surfaces

Example: Intersection of two surfaces

library(plot3Drgl)

x_domain <- seq(-2, 2, length.out = 150)
y_domain <- seq(-2, 2, length.out = 150)

elliptic_paraboloid <- function(x, y) x^2 + 2*y^2
z_elliptic <- outer(x_domain, y_domain, elliptic_paraboloid)

parabolic_cylinder <- function(x, y) 2 - x^2
z_parabolic <- outer(x_domain, y_domain, parabolic_cylinder)

persp3Drgl(z = z_elliptic, col = "orange")
persp3Drgl(z = z_parabolic, add = TRUE, col = "blue")
planes3d(0, 0, 1, 0, col = "lightgray")