asymptote: graph3
8.31 'graph3'
=============
This module implements three-dimensional versions of the functions in
'graph.asy'. To draw an x axis in three dimensions, use the routine
void xaxis3(picture pic=currentpicture, Label L="", axis axis=YZZero,
real xmin=-infinity, real xmax=infinity, pen p=currentpen,
ticks3 ticks=NoTicks3, arrowbar3 arrow=None, bool above=false);
Analogous routines 'yaxis' and 'zaxis' can be used to draw y and z axes
in three dimensions. There is also a routine for drawing all three
axis:
void axes3(picture pic=currentpicture,
Label xlabel="", Label ylabel="", Label zlabel="",
bool extend=false,
triple min=(-infinity,-infinity,-infinity),
triple max=(infinity,infinity,infinity),
pen p=currentpen, arrowbar3 arrow=None);
The predefined three-dimensional axis types are
axis YZEquals(real y, real z, triple align=O, bool extend=false);
axis XZEquals(real x, real z, triple align=O, bool extend=false);
axis XYEquals(real x, real y, triple align=O, bool extend=false);
axis YZZero(triple align=O, bool extend=false);
axis XZZero(triple align=O, bool extend=false);
axis XYZero(triple align=O, bool extend=false);
axis Bounds(int type=Both, int type2=Both, triple align=O, bool extend=false);
The optional 'align' parameter to these routines can be used to specify
the default axis and tick label alignments. The 'Bounds' axis accepts
two type parameters, each of which must be one of 'Min', 'Max', or
'Both'. These parameters specify which of the four possible
three-dimensional bounding box edges should be drawn.
The three-dimensional tick options are 'NoTicks3', 'InTicks',
'OutTicks', and 'InOutTicks'. These specify the tick directions for the
'Bounds' axis type; other axis types inherit the direction that would be
used for the 'Bounds(Min,Min)' axis.
Here is an example of a helix and bounding box axes with ticks and
axis labels, using orthographic projection:
import graph3;
size(0,200);
size3(200,IgnoreAspect);
currentprojection=orthographic(4,6,3);
real x(real t) {return cos(2pi*t);}
real y(real t) {return sin(2pi*t);}
real z(real t) {return t;}
path3 p=graph(x,y,z,0,2.7,operator ..);
draw(p,Arrow3);
scale(true);
xaxis3(XZ()*"$x$",Bounds,red,InTicks(Label,2,2));
yaxis3(YZ()*"$y$",Bounds,red,InTicks(beginlabel=false,Label,2,2));
zaxis3(XZ()*"$z$",Bounds,red,InTicks);
[helix]
The next example illustrates three-dimensional x, y, and z axes,
without autoscaling of the axis limits:
import graph3;
size(0,200);
size3(200,IgnoreAspect);
currentprojection=perspective(5,2,2);
scale(Linear,Linear,Log);
xaxis3("$x$",0,1,red,OutTicks(2,2));
yaxis3("$y$",0,1,red,OutTicks(2,2));
zaxis3("$z$",1,30,red,OutTicks(beginlabel=false));
[axis3]
One can also place ticks along a general three-dimensional axis:
import graph3;
size(0,100);
path3 g=yscale3(2)*unitcircle3;
currentprojection=perspective(10,10,10);
axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false),
ticklocate(0,360,new real(real v) {
path3 h=O--max(abs(max(g)),abs(min(g)))*dir(90,v);
return intersect(g,h)[0];},
new triple(real t) {return cross(dir(g,t),Z);}));
[generalaxis3]
Surface plots of matrices and functions over the region 'box(a,b)' in
the XY plane are also implemented:
surface surface(real[][] f, pair a, pair b, bool[][] cond={});
surface surface(real[][] f, pair a, pair b, splinetype xsplinetype,
splinetype ysplinetype=xsplinetype, bool[][] cond={});
surface surface(real[][] f, real[] x, real[] y,
splinetype xsplinetype=null, splinetype ysplinetype=xsplinetype,
bool[][] cond={})
surface surface(triple[][] f, bool[][] cond={});
surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx,
bool cond(pair z)=null);
surface surface(real f(pair z), pair a, pair b, int nx=nmesh, int ny=nx,
splinetype xsplinetype, splinetype ysplinetype=xsplinetype,
bool cond(pair z)=null);
surface surface(triple f(pair z), real[] u, real[] v,
splinetype[] usplinetype, splinetype[] vsplinetype=Spline,
bool cond(pair z)=null);
surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu,
bool cond(pair z)=null);
surface surface(triple f(pair z), pair a, pair b, int nu=nmesh, int nv=nu,
splinetype[] usplinetype, splinetype[] vsplinetype=Spline,
bool cond(pair z)=null);
The final two versions draw parametric surfaces for a function f(u,v)
over the parameter space 'box(a,b)', as illustrated in the example
'parametricsurface.asy'. An optional splinetype 'Spline' may be
specified. The boolean array or function 'cond' can be used to control
which surface mesh cells are actually drawn (by default all mesh cells
over 'box(a,b)' are drawn). Surface lighting is illustrated in the
example files 'parametricsurface.asy' and 'sinc.asy'. Lighting can be
disabled by setting 'light=nolight', as in this example of a Gaussian
surface:
import graph3;
size(200,0);
currentprojection=perspective(10,8,4);
real f(pair z) {return 0.5+exp(-abs(z)^2);}
draw((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle);
draw(arc(0.12Z,0.2,90,60,90,25),ArcArrow3);
surface s=surface(f,(-1,-1),(1,1),nx=5,Spline);
xaxis3(Label("$x$"),red,Arrow3);
yaxis3(Label("$y$"),red,Arrow3);
zaxis3(XYZero(extend=true),red,Arrow3);
draw(s,lightgray,meshpen=black+thick(),nolight,render(merge=true));
label("$O$",O,-Z+Y,red);
[GaussianSurface]
A mesh can be drawn without surface filling by specifying 'nullpen' for
the surfacepen.
A vector field of 'nu'\times'nv' arrows on a parametric surface 'f'
over 'box(a,b)' can be drawn with the routine
picture vectorfield(path3 vector(pair v), triple f(pair z), pair a, pair b,
int nu=nmesh, int nv=nu, bool truesize=false,
real maxlength=truesize ? 0 : maxlength(f,a,b,nu,nv),
bool cond(pair z)=null, pen p=currentpen,
arrowbar3 arrow=Arrow3, margin3 margin=PenMargin3)
as illustrated in the examples 'vectorfield3.asy' and
'vectorfieldsphere.asy'.
Info Catalog
asymptote: obj
asymptote: Base modules
asymptote: grid3