Data Point Plots

3D-plot windows interpret a vector of three numbers as the coordinates of a data point. The coordinate system selected by the Set > Coordinate System commandI8C1RB determines the meaning of coordinate vectors as follows:

• In rectangular coordinates, the coordinate vector [x, y, z] represents the point x units from the y-z plane, y units from the x-z plane, and z units from the x-y plane.

• In spherical coordinates, the coordinate vector [r, θ, φ] represents the point r units from the origin, θ radians from the positive x-axis, and φ radians from the positive z-axis.

• In cylindrical coordinates, the coordinate vector [r, θ, z] represents the point r units from the z-axis, θ radians from the positive x-axis, and z units from the x-y plane.

In the 3D-plot window, the form of the vector or matrix of coordinate vectors being plotted determines how the data is displayed. If xi, yi, and zi are numerical constants, the following summarizes how such vectors and matrices are plotted:

• Both the coordinate vector [x, y, z] and the 1 by 3 matrix of coordinate values [[x, y, z]] each plot as a single isolated point.

• The vector of n 1 by 3 matrices of coordinate values [[x1, y1, z1]; [x2, y2, z2]; ...; [xn, yn, zn]] plots as n isolated points. For example, in rectangular coordinates

[[0, 0, 0]; [2, 0, 0]; [0, 2, 0]]

plots as three points in the x-y plane.

• The n by 3 matrix of coordinate values [x1, y1, z1; x2, y2, z2; ...; xn, yn, zn] plots as n-1 connected line segments. For example, in rectangular coordinates

[0, 0, 0; 2, 0, 0; 0, 2, 0; 0, 0, 0]

plots as a triangle in the x-y plane.

• The n by m matrix of z-values [z11, z12, ..., z1m; z21, z22, ..., z2m; ...; zn1, zn2, ..., znm] plots as the functional surface defined by the n·m rectangular coordinate vectors [i, j, zij]. For example, if the Approximate Before PlottingEVZ132 option is turned on,

VECTOR(VECTOR(SIN(x) + COS(y), x, -10, 10), y, -10, 10)

plots as the undulating surface z = sin x + cos y. Note that if m (i.e. the number of columns) is 3, data matrices of this form are plotted as n-1 connected line segments as described above.

• The n by m matrix of coordinate vectors

[ x11, y11, z11; x12, y12, z12; ...; x1m, y1m, z1m ]

[ x21, y21, z21; x22, y22, z22; ..., x2m, y2m, z2m ]
...
[ xn1, yn1, zn1; xn2, yn2, zn2; ...; xnm, ynm, znm ]

plots as the parametric surface defined by the n·m coordinate vectors [xij, yij, zij]. For example, in rectangular coordinates

[[ 3, 3, 3; 3, 3, -3],
[ 3, -3, 3; 3, -3, -3],
[-3, -3, 3; -3, -3, -3],
[-3, 3, 3; -3, 3, -3],
[ 3, 3, 3; 3, 3, -3]]

plots as an open ended box.