Plot 2D¶
# Copyright (c) 2018-2025 William Emerison Six
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place - Suite 330,
# Boston, MA 02111-1307, USA.
Problem 1¶
import math
import sympy
from modelviewprojection.mathutils import (
Vector1D,
Vector2D,
Vector3D,
compose,
compose_intermediate_fns,
identity,
inverse,
)
from modelviewprojection.mathutils import rotate as R
from modelviewprojection.mathutils import scale_non_uniform_2d as S
from modelviewprojection.mathutils import translate as T
from modelviewprojection.nbplotutils import (
create_basis,
create_graphs,
create_unit_circle,
create_x_and_y,
draw_isoceles_triangle,
draw_right_triangle,
draw_screen,
draw_second_right_triangle,
)
T(Vector1D(5))
\[T_{<[5]>}\]
S(5, 6)
\[S_{<5,6>}\]
inverse(T(Vector1D(5)))
\[T_{<[-5]>}\]
T(Vector2D(5, 6))
\[T_{<[5, 6]>}\]
T(Vector3D(5, 6, 7))
\[T_{<[5, 6, 7]>}\]
inverse(T(Vector3D(5, 6, 7)))
\[T_{<[-5, -6, -7]>}\]
R(sympy.pi / 2)
\[R_{<\frac{\pi}{2}>}\]
compose([R(sympy.pi / 2), T(Vector2D(5, 6))])
\[R_{<\frac{\pi}{2}>} \circ T_{<[5, 6]>}\]
inverse(compose([R(sympy.pi / 2), T(Vector2D(5, 6))]))
\[T_{<[-5, -6]>} \circ R_{<- \frac{\pi}{2}>}\]
Draw graph paper¶
Just draw graph paper, where one unit in the x direction is blue, and one unit in the y direction is pink. The graph paper corresponds to the numbers on the left and on the bottom.
fn = R(math.radians(53.130102))
with create_graphs(graph_bounds=(5, 5)) as axes:
create_basis(fn=fn)
create_x_and_y(fn=fn)
create_unit_circle(fn=fn)
axes.set_title(fn._repr_latex_())
Draw relative graph paper¶
Draw two relative number lines, making a relative graph paper, but keep the original coordinate system on the left and bottom. Any point in the plane can be described using two different graph papers.
fn = R(math.radians(53.130102))
with create_graphs(graph_bounds=(5, 5)) as axes:
create_basis(fn=R(0.0))
create_x_and_y(fn=R(0.0))
create_basis(
fn=fn,
xcolor=(0, 1, 0),
ycolor=(1, 1, 0),
)
create_x_and_y(
fn=fn,
xcolor=(0, 1, 0),
ycolor=(1, 1, 0),
)
create_unit_circle(fn=fn)
axes.set_title(fn._repr_latex_())
Draw relative graph paper¶
Draw two relative number lines, making a relative graph paper, but keep the original coordinate system on the left and bottom. Any point in the plane can be described using two different graph papers.
fn = R(math.radians(53.130102))
with create_graphs(graph_bounds=(5, 5)) as axes:
create_basis(fn=R(0.0))
create_x_and_y(fn=R(0.0))
create_basis(
fn=fn,
xcolor=(0, 1, 0),
ycolor=(1, 1, 0),
)
create_x_and_y(
fn=fn,
xcolor=(0, 1, 0),
ycolor=(1, 1, 0),
)
create_unit_circle(fn=fn)
draw_right_triangle()
draw_second_right_triangle()
axes.set_title(fn._repr_latex_())
Draw relative graph paper, defined by composed functions¶
Draw a translated and rotated graph paper. You can read the sequence of composed functions in the order that they are applied, or in reverse order
fn = compose(
[
R(sympy.pi / 4),
T(Vector2D(x=2.0, y=0.0)),
]
)
with create_graphs() as axes:
create_basis(
fn=fn,
)
create_x_and_y(fn=fn)
create_unit_circle(fn=fn)
axes.set_title(fn._repr_latex_())
Composed functions, read bottom up¶
The sequence of functions shown, where the translate is applied first, and operations are relative to the units on the left and bottom.
for f in compose_intermediate_fns([R(sympy.pi / 4), T(Vector2D(x=2.0, y=0.0))]):
# TODO - figure out if I can render the latex as part of one markdown command,
# if I were to uncomment out this line and other markdown lines,
# the build of HTML would fail
with create_graphs() as axes:
create_basis(fn=f)
create_x_and_y(fn=f)
create_x_and_y()
draw_isoceles_triangle(fn=f)
create_unit_circle(fn=f)
create_unit_circle()
axes.set_title(f._repr_latex_())
Composed functions, read top down¶
The sequence of functions shown, where we visualize the rotate first, and then the translate relative to that relative graph paper.
for f in compose_intermediate_fns(
[
R(sympy.pi / 4),
T(Vector2D(x=1.0, y=0.0)),
],
relative_basis=True,
):
with create_graphs() as axes:
create_basis(fn=f)
create_x_and_y(fn=f)
draw_isoceles_triangle(fn=f)
create_unit_circle(fn=f)
axes.set_title(f._repr_latex_())
screen_width: int = 4
screen_height: int = 3
for f in compose_intermediate_fns(
[
T(Vector2D(-0.5, -0.5)),
S(screen_width, screen_height),
S(0.5, 0.5),
T(Vector2D(x=1.0, y=1.0)),
],
relative_basis=False,
):
with create_graphs(graph_bounds=(6, 6)) as axes:
# create_basis(fn=f)
# create_x_and_y(fn=f)
create_basis(fn=identity())
create_x_and_y(fn=identity())
# draw_ndc(fn=f)
draw_screen(width=screen_width, height=screen_height, fn=f)
axes.set_title(f._repr_latex_())
screen_width: int = 4
screen_height: int = 3
for f in compose_intermediate_fns(
[
T(Vector2D(-0.5, -0.5)),
S(screen_width, screen_height),
S(0.5, 0.5),
T(Vector2D(x=1.0, y=1.0)),
],
relative_basis=True,
):
with create_graphs(graph_bounds=(6, 6)) as axes:
# create_basis(fn=f)
# create_x_and_y(fn=f)
create_basis(fn=identity())
create_x_and_y(fn=f)
# draw_ndc(fn=f)
draw_screen(width=screen_width, height=screen_height, fn=f)
axes.set_title(f._repr_latex_())
