misc3d (version 0.9-1)

parametric3d: Draw a 3D Parametric Plot

Description

Plot a two-parameter surface in three dimensions.

Usage

parametric3d(fx, fy, fz, u, v, umin, umax, vmin, vmax, n = 100,
               color = "white", color2 = NA, alpha = 1,
               fill = TRUE, col.mesh = if (fill) NA else color,
               smooth = 0, material = "default", 
               add = FALSE, draw = TRUE, engine = "rgl", ...)

Arguments

fx,fy,fz

vectorized functions of u and v to compute the x, y, and z coordinates.

u

numeric vector of u values.

v

numeric vector of v values.

umin

numeric; the minimum value of u. Ignored if u is supplied.

umax

numeric; the maximum value of u. Ignored if u is supplied.

vmin

numeric; the minimum value of v. Ignored if v is supplied.

vmax

numeric; the maximum value of v. Ignored if v is supplied.

n

the number of equally spaced u and v values to use. Ignored if u and v are supplied.

color

color to use for the surface. Can also be a function of three arguments. This is called with three arguments, the coordinates of the midpoints of the triangles making up the surface. The function should return a vector of colors to use for the triangles.

color2

opposite face color.

alpha

alpha channel level, a number between 0 and 1..

fill

logical; if TRUE, drawing should use filled surfaces; otherwise a wire frame should be drawn.

col.mesh

color to use for the wire frame.

smooth

integer or logical specifying Phong shading level for "standard" and "grid" engines or whether or not to use shading for the "rgl" engine.

material

material specification; currently only used by "standard" and "grid" engines. Currently possible values are the character strings "dull", "shiny", "metal", and "default".

add

logical; if TRUE, add to current graph.

draw

logical; if TRUE, draw the results; otherwise, return triangle mesh structure.

engine

character; currently "rgl", "standard", "grid" or "none"; for "none" the computed triangles are returned.

...

additional rendering arguments, e.g. material and texture properties for the "rgl" engine. See documentation for drawScene and drawScene.rgl

Value

For the "rgl" engine the returned value is NULL. For the "standard" and "grid" engines the returned value is the viewing transformation as returned by persp. For the engine "none", or when draw is not true, the returned value is a structure representing the triangles making up the surface.

Details

Analogous to Mathematica's Param3D. Evaluates the functions fx, fy, and fz specifying the coordinates of the surface at a grid of values for the parameters u and v.

References

Daniel Adler, Oleg Nenadic and Walter Zucchini (2003) RGL: A R-library for 3D visualization with OpenGL

See Also

surface3d, material3d,scatterplot3d.

Examples

# NOT RUN {
  #Example 1: Ratio-of-Uniform sampling region of bivariate normal
  parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
                      2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
               fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
                      2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
               fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u * 
                      v)/sqrt(1-.75^2))^(1/3),
               umin = -20, umax = 20, vmin = -20, vmax = 20, 
               n = 100)	
  parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
                      2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
               fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
                      2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
               fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u * 
                      v)/sqrt(1-.75^2))^(1/3),
               u = qcauchy((1:100)/101), v = qcauchy((1:100)/101))	
  parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
                      2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
               fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
                      2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
               fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u * 
                      v)/sqrt(1-.75^2))^(1/3),
               u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
               engine = "standard", scale = FALSE, screen = list(x=-90, y=20))

  #Example 2: Ratio-of-Uniform sampling region of Bivariate t      
  parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3), 
               fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
               fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3), 
               umin = -20, umax = 20, vmin = -20, vmax = 20, 
               n = 100, color = "green")
  parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
               fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
               fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
               u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
               color = "green")
  parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
               fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
               fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
               u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
               color = "green", engine = "standard", scale = FALSE)


  #Example 3: Surface of revolution
  parametric3d(fx = function(u,v) u,
               fy = function(u,v) sin(v)*(u^3+2*u^2-2*u+2)/5,
               fz = function(u,v) cos(v)*(u^3+2*u^2-2*u+2)/5,
               umin = -2.3, umax = 1.3, vmin = 0, vmax = 2*pi)
  parametric3d(fx = function(u,v) u,
               fy = function(u,v) sin(v)*(u^3+2*u^2-2*u+2)/5,
               fz = function(u,v) cos(v)*(u^3+2*u^2-2*u+2)/5,
               umin = -2.3, umax = 1.3, vmin = 0, vmax = 2*pi,
               engine = "standard", scale = FALSE,
               color = "red", color2 = "blue", material = "shiny")

# }