parametric3d: Draw a 3D Parametric Plot

In misc3d: Miscellaneous 3D Plots

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

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.

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.

Note

The "rgl" engine now uses the standard rgl coordinates instead of negating y and swapping y and z. If you need to reproduce the previous behavior you can use options(old.misc3d.orientation=TRUE).

Transparency only works properly in the "rgl" engine. For standard or grid graphics on pdf or quartz devices using alpha levels less than 1 does work but the triangle borders show as a less transparent mesh.

References

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

See Also

surface3d, material3d,scatterplot3d.

Examples

  #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")

misc3d documentation built on Oct. 8, 2021, 1:06 a.m.