### The Maxima on-line user's manual

Algebra Calculator

#### Points

-- Graphic object: points ([[<x1>,<y1>], [<x2>,<y2>],...]) -- Graphic object: points ([<x1>,<x2>,...], [<y1>,<y2>,...]) -- Graphic object: points ([<y1>,<y2>,...]) -- Graphic object: points ([[<x1>,<y1>,<z1>], [<x2>,<y2>,<z2>],...]) -- Graphic object: points ([<x1>,<x2>,...], [<y1>,<y2>,...], [<z1>,<z2>,...]) -- Graphic object: points (<matrix>) -- Graphic object: points (<1d_y_array>) -- Graphic object: points (<1d_x_array>, <1d_y_array>) -- Graphic object: points (<1d_x_array>, <1d_y_array>, <1d_z_array>) -- Graphic object: points (<2d_xy_array>) -- Graphic object: points (<2d_xyz_array>) Draws points in 2D and 3D.

This object is affected by the following graphic options: `point_size`, `point_type`, `points_joined`, `line_width`, `key`, `line_type` and `color`. In 3D mode, it is also affected by `enhanced3d`.

2D

`points ([[<x1>,<y1>], [<x2>,<y2>],...])` or `points ([<x1>,<x2>,...], [<y1>,<y2>,...])` plots points `[x1,y1]`, `[x2,y2]`, etc. If abscissas are not given, they are set to consecutive positive integers, so that `points ([<y1>,<y2>,...])` draws points `[1,<y1>]`, `[2,<y2>]`, etc. If <matrix> is a two-column or two-row matrix, `points (<matrix>)` draws the associated points. If <matrix> is a one-column or one-row matrix, abscissas are assigned automatically.

If <1d_y_array> is a 1D lisp array of numbers, `points (<1d_y_array>)` plots them setting abscissas to consecutive positive integers. `points (<1d_x_array>, <1d_y_array>)` plots points with their coordinates taken from the two arrays passed as arguments. If <2d_xy_array> is a 2D array with two columns, or with two rows, `points (<2d_xy_array>)` plots the corresponding points on the plane.

Examples:

Two types of arguments for `points`, a list of pairs and two lists of separate coordinates.

`          (%i1) load(draw)\$`
`          (%i2) draw2d(`
`                  key = "Small points",`
`                  points(makelist([random(20),random(50)],k,1,10)),`
`                  point_type    = circle,`
`                  point_size    = 3,`
`                  points_joined = true,`
`                  key           = "Great points",`
`                  points(makelist(k,k,1,20),makelist(random(30),k,1,20)),`
`                  point_type    = filled_down_triangle,`
`                  key           = "Automatic abscissas",`
`                  color         = red,`
`                  points([2,12,8]))\$`

```     Drawing impulses.
(%i2) draw2d(
points_joined = impulses,
line_width    = 2,
color         = red,
points(makelist([random(20),random(50)],k,1,10)))\$```

```     Array with ordinates.
(%i2) a: make_array (flonum, 100) \$
(%i3) for i:0 thru 99 do a[i]: random(1.0) \$
(%i4) draw2d(points(a)) \$```

```     Two arrays with separate coordinates.
(%i2) x: make_array (flonum, 100) \$
(%i3) y: make_array (fixnum, 100) \$
(%i4) for i:0 thru 99 do (
x[i]: float(i/100),
y[i]: random(10) ) \$
(%i5) draw2d(points(x, y)) \$```

```     A two-column 2D array.
(%i2) xy: make_array(flonum, 100, 2) \$
(%i3) for i:0 thru 99 do (
xy[i, 0]: float(i/100),
xy[i, 1]: random(10) ) \$
(%i4) draw2d(points(xy)) \$```

```     Drawing an array filled with function `read_array`.
(%i2) a: make_array(flonum,100) \$
(%i3) read_array (file_search ("pidigits.data"), a) \$
(%i4) draw2d(points(a)) \$```

3D

`points ([[<x1>,<y1>,<z1>], [<x2>,<y2>,<z2>],...])` or `points ([<x1>,<x2>,...], [<y1>,<y2>,...], [<z1>,<z2>,...])` plots points `[<x1>,<y1>,<z1>]`, `[<x2>,<y2>,<z2>]`, etc. If <matrix> is a three-column or three-row matrix, `points (<matrix>)` draws the associated points.

When arguments are lisp arrays, `points (<1d_x_array>, <1d_y_array>, <1d_z_array>)` takes coordinates from the three 1D arrays. If <2d_xyz_array> is a 2D array with three columns, or with three rows, `points (<2d_xyz_array>)` plots the corresponding points.

Examples:

```     One tridimensional sample,
(%i3) s2 : read_matrix (file_search ("wind.data"))\$
(%i4) draw3d(title = "Daily average wind speeds",
point_size = 2,
points(args(submatrix (s2, 4, 5))) )\$```

```     Two tridimensional samples,
(%i3) s2 : read_matrix (file_search ("wind.data"))\$
(%i4) draw3d(
title = "Daily average wind speeds. Two data sets",
point_size = 2,
key        = "Sample from stations 1, 2 and 3",
points(args(submatrix (s2, 4, 5))),
point_type = 4,
key        = "Sample from stations 1, 4 and 5",
points(args(submatrix (s2, 2, 3))) )\$```

```     Unidimensional arrays,
(%i2) x: make_array (fixnum, 10) \$
(%i3) y: make_array (fixnum, 10) \$
(%i4) z: make_array (fixnum, 10) \$
(%i5) for i:0 thru 9 do (
x[i]: random(10),
y[i]: random(10),
z[i]: random(10) ) \$
(%i6) draw3d(points(x,y,z)) \$```

```     Bidimensional colored array,
(%i2) xyz: make_array(fixnum, 10, 3) \$
(%i3) for i:0 thru 9 do (
xyz[i, 0]: random(10),
xyz[i, 1]: random(10),
xyz[i, 2]: random(10) ) \$
(%i4) draw3d(
enhanced3d = true,
points_joined = true,
points(xyz)) \$```

There are also some inexact matches for `points`. Try `?? points` to see them.

```(%o1)                                true
(%i2) ```

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