The parametric_plots library

The parametric_plots library is part of the graphics library.

Example

import geometry;
import graphics;
import graphics/parametric_plots;

define plot =
    begin
        scene := empty_scene("plot");

        fun := (u, v) -> vector3d(u,v, 1/(u*v));

        range := make_range(-5, 5, -5, 5);

        options := default_parametric_plot_options;
        options := with_parametric_plot_options_n(50, options);
        
        scene := plot_parametric_surface(fun, range, options, scene);
        scene := plot_parametric_surface_grid(fun, range, options, scene);

        return scene;
    end;

Use the pacioli_scene web-component to display the plot in a web-page.

Synopsis

default_parametric_plot_options :: ParametricPlotOptions

interval_length :: for_unit a: (Interval(a)) -> a
interval_lower :: for_unit a: (Interval(a)) -> a
interval_upper :: for_unit a: (Interval(a)) -> a
make_interval :: for_unit a: (a, a) -> Interval(a)
make_parametric_plot_options :: (1, 1, 1, 1, Boole, Boole, Boole, Boole, String, Color, Color, Color) -> ParametricPlotOptions
make_range :: for_unit a, b: (a, a, b, b) -> Range2D(a, b)
make_range2d :: for_unit a, b: (Interval(a), Interval(b)) -> Range2D(a, b)
parametric_plot_options_color :: (ParametricPlotOptions) -> Color
parametric_plot_options_delta_color :: (ParametricPlotOptions) -> Color
parametric_plot_options_m :: (ParametricPlotOptions) -> 1
parametric_plot_options_n :: (ParametricPlotOptions) -> 1
parametric_plot_options_normal_color :: (ParametricPlotOptions) -> Color
parametric_plot_options_scale_factor :: (ParametricPlotOptions) -> 1
parametric_plot_options_show_normals :: (ParametricPlotOptions) -> Boole
parametric_plot_options_show_parts :: (ParametricPlotOptions) -> Boole
parametric_plot_options_show_total :: (ParametricPlotOptions) -> Boole
parametric_plot_options_wireframe :: (ParametricPlotOptions) -> Boole
plot_parametric_path :: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, a, b, a, b, ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)
plot_parametric_surface :: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, Range2D(a, b), ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)
plot_parametric_surface_deltas :: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, Range2D(a, b), ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)
plot_parametric_surface_grid :: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, Range2D(a, b), ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)
range2d_u :: for_unit a, b: (Range2D(a, b)) -> Interval(a)
range2d_v :: for_unit a, b: (Range2D(a, b)) -> Interval(b)
range_height :: for_unit a, b: (Range2D(a, b)) -> b
range_ustart :: for_unit a, b: (Range2D(a, b)) -> a
range_vstart :: for_unit a, b: (Range2D(a, b)) -> b
range_width :: for_unit a, b: (Range2D(a, b)) -> a
scale_interval :: for_unit a, b: (a, Interval(b)) -> Interval(a*b)
scale_range :: for_unit a, b, c, d: (a, b, Range2D(c, d)) -> Range2D(a*c, b*d)
with_interval_lower :: for_unit a: (a, Interval(a)) -> Interval(a)
with_interval_upper :: for_unit a: (a, Interval(a)) -> Interval(a)
with_parametric_plot_options_color :: (Color, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_delta_color :: (Color, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_m :: (1, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_n :: (1, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_normal_color :: (Color, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_scale_factor :: (1, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_show_normals :: (Boole, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_show_parts :: (Boole, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_show_total :: (Boole, ParametricPlotOptions) -> ParametricPlotOptions
with_parametric_plot_options_wireframe :: (Boole, ParametricPlotOptions) -> ParametricPlotOptions
with_range2d_u :: for_unit a, b: (Interval(a), Range2D(a, b)) -> Range2D(a, b)
with_range2d_v :: for_unit a, b: (Interval(b), Range2D(a, b)) -> Range2D(a, b)

Types

ParametricPlotOptions

ParametricPlotOptions

Options for plotting parametric surfaces, grids and deltas.

Values

default_parametric_plot_options

:: ParametricPlotOptions

Default values for the options for parametric plots.

Functions

interval_length

:: for_unit a: (Interval(a)) -> a

interval_lower

:: for_unit a: (Interval(a)) -> a

Getter for record Interval(a)

interval_upper

:: for_unit a: (Interval(a)) -> a

Getter for record Interval(a)

make_interval

:: for_unit a: (a, a) -> Interval(a)

Constructor for record Interval(a)

make_parametric_plot_options

:: (1, 1, 1, 1, Boole, Boole, Boole, Boole, String, Color, Color, Color) -> ParametricPlotOptions

Constructor for record ParametricPlotOptions

make_range

:: for_unit a, b: (a, a, b, b) -> Range2D(a, b)

make_range2d

:: for_unit a, b: (Interval(a), Interval(b)) -> Range2D(a, b)

Constructor for record Range2D(a, b)

parametric_plot_options_color

:: (ParametricPlotOptions) -> Color

Getter for record ParametricPlotOptions

parametric_plot_options_delta_color

:: (ParametricPlotOptions) -> Color

Getter for record ParametricPlotOptions

parametric_plot_options_m

:: (ParametricPlotOptions) -> 1

Getter for record ParametricPlotOptions

parametric_plot_options_n

:: (ParametricPlotOptions) -> 1

Getter for record ParametricPlotOptions

parametric_plot_options_normal_color

:: (ParametricPlotOptions) -> Color

Getter for record ParametricPlotOptions

parametric_plot_options_scale_factor

:: (ParametricPlotOptions) -> 1

Getter for record ParametricPlotOptions

parametric_plot_options_show_normals

:: (ParametricPlotOptions) -> Boole

Getter for record ParametricPlotOptions

parametric_plot_options_show_parts

:: (ParametricPlotOptions) -> Boole

Getter for record ParametricPlotOptions

parametric_plot_options_show_total

:: (ParametricPlotOptions) -> Boole

Getter for record ParametricPlotOptions

parametric_plot_options_wireframe

:: (ParametricPlotOptions) -> Boole

Getter for record ParametricPlotOptions

plot_parametric_path

:: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, a, b, a, b, ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)

plot_parametric_surface

:: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, Range2D(a, b), ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)

Plots a parametric surface in a 3D space.

The function parameter is a function from the given range to Geom3 vectors. The function is sampled for the given range to give the surface points.

The number of samples, and other parameters like color, can be set in the options.

For example

let
    u_interval = make_interval(-5*|metre|, 5*|metre|),  
    v_interval = make_interval(-5*|metre|, 5*|metre|)
in  
    plot_parametric_surface(
        (u, v) -> vector3d(u, v, 3*|metre| - 0.5*u - 0.2*v),
        make_range2d(u_interval, v_interval),
        default_parametric_plot_options,
        scene)
end

plots a part of a plane, using default options. It yields a scene of type Scene(metre, Geom3!)

plot_parametric_surface_deltas

:: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, Range2D(a, b), ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)

plot_parametric_surface_grid

:: for_unit a, b, c, Geom3!u: ((a, b) -> c*Geom3!u, Range2D(a, b), ParametricPlotOptions, Scene(c, Geom3!u)) -> Scene(c, Geom3!u)

Plots a parametric grid in a 3D space.

The function parameter is a function from the given range to Geom3 vectors. The function is sampled for the given range to give the grid points.

The number of samples, and other parameters like color, can be set in the options.

It is similar to plotting a surface using plot_parametric_surface with the option wireframe, but it displays rectangles instead of triangles.

range2d_u

:: for_unit a, b: (Range2D(a, b)) -> Interval(a)

Getter for record Range2D(a, b)

range2d_v

:: for_unit a, b: (Range2D(a, b)) -> Interval(b)

Getter for record Range2D(a, b)

range_height

:: for_unit a, b: (Range2D(a, b)) -> b

range_ustart

:: for_unit a, b: (Range2D(a, b)) -> a

range_vstart

:: for_unit a, b: (Range2D(a, b)) -> b

range_width

:: for_unit a, b: (Range2D(a, b)) -> a

scale_interval

:: for_unit a, b: (a, Interval(b)) -> Interval(a*b)

scale_range

:: for_unit a, b, c, d: (a, b, Range2D(c, d)) -> Range2D(a*c, b*d)

with_interval_lower

:: for_unit a: (a, Interval(a)) -> Interval(a)

Setter for record Interval(a)

with_interval_upper

:: for_unit a: (a, Interval(a)) -> Interval(a)

Setter for record Interval(a)