diff --git a/docs/build/html/pylib.data.html b/docs/build/html/pylib.data.html
index af92f00..b86eb6f 100644
--- a/docs/build/html/pylib.data.html
+++ b/docs/build/html/pylib.data.html
@@ -83,6 +83,39 @@ array. m = k / n
+
+
+issequence( obj ) [source]
+True for tuple, list, str
+False for int, dict, set
+
+Example
+
+>>> issequence (())
+True
+>>> issequence (( 3 , ))
+True
+>>> issequence ([])
+True
+>>> issequence ([ 1 ])
+True
+>>> issequence ([ 1 , 2 ])
+True
+>>> issequence ( '' )
+True
+
+
>>> issequence (( 3 ))
+False
+>>> issequence ({})
+False
+>>> issequence ( set ())
+False
+
+
+
load( file_name , default=None , verbose=False ) [source]
diff --git a/docs/build/html/pylib.function.html b/docs/build/html/pylib.function.html
index 96a622a..8935d16 100644
--- a/docs/build/html/pylib.function.html
+++ b/docs/build/html/pylib.function.html
@@ -172,7 +172,7 @@ y(\theta) = (R - r)\sin\theta - d\sin\left(\frac{R-r}{r}\theta\right) \\
@@ -359,7 +359,7 @@ Example of 3 columns and 3 rows (upside down view of ‘normal’ braille/drawil
diff --git a/docs/build/html/pylib.geometry.html b/docs/build/html/pylib.geometry.html
index cdf6301..3861f74 100644
--- a/docs/build/html/pylib.geometry.html
+++ b/docs/build/html/pylib.geometry.html
@@ -36,16 +36,23 @@
pylib.geometry module
-
2D geometry objects.
+
Geometry objects.
Date
2019-12-21
-
+
diff --git a/docs/build/html/pylib.geometry2d.html b/docs/build/html/pylib.geometry2d.html
index 7ccc9f6..14f9ac1 100644
--- a/docs/build/html/pylib.geometry2d.html
+++ b/docs/build/html/pylib.geometry2d.html
@@ -276,7 +276,7 @@ decides what the left and the right end point of the line is.
See also
-
plot_lines() geometry_plot
plot_lines() geometry_plot
diff --git a/docs/build/html/pylib.geometry2d_plot.html b/docs/build/html/pylib.geometry2d_plot.html
index e17c8dc..0ff8944 100644
--- a/docs/build/html/pylib.geometry2d_plot.html
+++ b/docs/build/html/pylib.geometry2d_plot.html
@@ -16,7 +16,7 @@
pylib pylib.geometry_plot module — pylib 2019.12.21 documentation
+
+
+
+
+
+
+
+
+
pylib.geometry_plot module
+
Geometry plotter using matplotlib (pylab).
+
+Date
+2019-12-23
+
+
+
+
+
+
+
+
+
+
+
pylib.geometry_plot_pylab module — pylib 2019.12.21 documentation
+
+
+
+
+
+
+
+
+
pylib.geometry_plot_pylab module
+
Geometry plotter using pylab (matplotlib).
+
+Date
+2019-12-23
+
+
+
+cad_wireframe( world , centering=True ) [source]
+Graphical projections
+
+Parallel projections
+
+Orthographic
+
+Multiview
+
+* First-angle
Third-angle
Plan Elevation
+Axonometric
+
+* Isometric
Dimetric
Trimetri
+
+Oblique
+
+Carbinet
Cavalier
Military
Top-down
+
+Perspective projections
+
+1-point
2-point
3-point
Curvilinear
+
+
+
+
+
+plot_post( ax ) [source]
+
+
+
+
+set_aspect_equal( ax ) [source]
+Make axes of 3D plot have equal scale so that spheres appear as
+spheres, cubes as cubes, etc.. This is one possible solution to
+Matplotlib’s ax.set_aspect(‘equal’) and ax.axis(‘equal’) not
+working for 3D.
+
+Parameters
+ax (pylab.Axes ) – a pylab axis
+
+Source: https://stackoverflow.com/a/35126679
+
+
+
+
+wireframe3d( world ) [source]
+
+
+
+
+
+
+
+
+
+
+
+
pylib.date module pylib.drawblock module pylib.function module pylib.geometry module pylib.geometry module
+pylib.geometry2d module pylib.geometry2d_plot module pylib.geometry_plot module pylib.geometry_plot_pylab module pylib.mathematics module pylib.time_of_day module class matrix[source] Bases: list
Use/create matrix like list of lists
+
+
+__getitem__( index ) [source]
+For index return value, for range return new vector object.
+
+Example
+
+>>> m = matrix ([[ 1 , 2 , 3 , 0 ], [ 4 , 5 , 6 , 0 ], [ 7 , 8 , 9 , 0 ], [ 0 , 0 , 0 , 0 ]])
+>>> print ( m [ 2 ])
+[7, 8, 9, 0]
+>>> print ( m [:, 1 : 3 ])
+[[2, 3], [5, 6], [8, 9], [0, 0]]
+>>> print ( m [ 0 : 2 , 1 : 3 ])
+[[2, 3], [5, 6]]
+>>> print ( m [:: 2 , :: 2 ])
+[[1, 3], [7, 9]]
+
+
+
+
+
+__mul__( other ) [source]
+Scalar multiplication, dot product (inner product) or
+matrix-vector multiplication. (new object)
+
+
+
+\[\begin{split}\mathbf{C} &= \mathbf{A} \cdot b \\
+\mathbf{c} &= \mathbf{A} \cdot \mathbf{b} \\
+\mathbf{C} &= \mathbf{A} \cdot \mathbf{B}\end{split}\]
+
+
Note
+
No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).
+
+Example
+
+>>> m = matrix ([[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ], [ 9 , 10 , 11 , 12 ], \
+ [0, 0, 0, 1]]) * 5
+>>> print ( m )
+[[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]
+>>> m = matrix ([[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ], [ 9 , 10 , 11 , 12 ], \
+ [0, 0, 0, 1]]) * 5.
+>>> print ( m )
+[[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]
+>>> v = matrix ([[ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ]]) * \
+ vector([12, 12, 13])
+>>> print ( v )
+[75, 186, 297]
+>>> m = matrix ([[ 1 , 2 , 3 ], [ 4 , 5 , 6 ], [ 7 , 8 , 9 ]]) * \
+ matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])
+>>> print ( m )
+[[91, 96, 102], [220, 231, 246], [349, 366, 390]]
+
+
+
+
+
+__repr__( ) [source]
+Return repr(self).
+
+
+
+
+__rmul__( other ) [source]
+Scalar multiplication, dot product (inner product) or
+vector-matrix multiplication. (new object)
+
+
+
+\[\begin{split}\mathbf{C} &= a \cdot \mathbf{B} \\
+\mathbf{c} &= \mathbf{a} \cdot \mathbf{B} \\
+\mathbf{C} &= \mathbf{A} \cdot \mathbf{B}\end{split}\]
+
+
Note
+
No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).
+
+Example
+
+>>> m = 5 * matrix ([[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ], \
+ [9, 10, 11, 12], [0, 0, 0, 1]])
+>>> print ( m )
+[[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]
+>>> m = 5. * matrix ([[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ], \
+ [9, 10, 11, 12], [0, 0, 0, 1]])
+>>> print ( m )
+[[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]
+
+
+
+
+
+__str__( ) [source]
+Return str(self).
+
+
rotate_x( theta ) [source]
@@ -134,7 +247,7 @@
Rotation matrix about the x direction.
Rotates the coordinate system of vectors
-\[\begin{split}R_{x}(\theta) =
+\[\begin{split}\mathbf{R}_{x}(\theta) =
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & \cos \theta & -\sin \theta & 0 \\
@@ -149,7 +262,7 @@
Rotation matrix about the y direction.
Rotates the coordinate system of vectors
-\[\begin{split}R_{y}(\theta) =
+\[\begin{split}\mathbf{R}_{y}(\theta) =
\begin{bmatrix}
\cos \theta & 0 & \sin \theta & 0 \\
0 & 1 & 0 & 0 \\
@@ -164,7 +277,7 @@
Rotation matrix about the z direction.
Rotates the coordinate system of vectors
-\[\begin{split}R_{z}(\theta) =
+\[\begin{split}\mathbf{R}_{z}(\theta) =
\begin{bmatrix}
\cos \theta & -\sin \theta & 0 & 0 \\
\sin \theta & \cos \theta & 0 & 0 \\
@@ -176,14 +289,17 @@
-\[\begin{split}R_{z}(\theta) \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+\[\begin{split}\mathbf{R}_{z}(\theta)
+\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix}
+&=
\begin{bmatrix}
\cos 90° & -\sin 90° & 0 & 0 \\
\sin 90° & \cos 90° & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}
-\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} \\
+&=
\begin{bmatrix}
0 & -1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
@@ -200,12 +316,12 @@
Scaling matrix
uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
-centered at the origin will have their centers move. To avoid this,
-either scale the object when it’s located at the origin, or
-perform a translation afterwards to move the object back to where
-it should be.
+centered at the origin will have their centers move. To avoid
+this, either scale the object when it’s located at the origin,
+or perform a translation afterwards to move the object back to
+where it should be.
-\[\begin{split}S =
+\[\begin{split}\mathbf{S} =
\begin{bmatrix}
s_x & 0 & 0 & 0 \\
0 & s_y & 0 & 0 \\
@@ -220,10 +336,10 @@ it should be.
Scaling
uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
-centered at the origin will have their centers move. To avoid this,
-either scale the object when it’s located at the origin, or
-perform a translation afterwards to move the object back to where
-it should be.
+centered at the origin will have their centers move. To avoid
+this, either scale the object when it’s located at the origin,
+or perform a translation afterwards to move the object back to
+where it should be.
\[\begin{split}\begin{bmatrix}
xx' & xy' & xz' & t_x' \\
@@ -250,7 +366,7 @@ it should be.
static t( tx ,
ty ,
tz ) [source] Translation matrix
-\[\begin{split}T =
+\[\begin{split}\mathbf{T} =
\begin{bmatrix}
1 & 0 & 0 & t_x \\
0 & 1 & 0 & t_y \\
@@ -292,60 +408,385 @@ it should be.
Bases: list
Use/create vector like lists
-size -> len(a)
abs -> abs(a)
dot -> a * b
outer -> a @ b
size, length of a vector use len(a)
absolute, magntude, norm of a vector use abs(a), see
+__abs__()
dot product use a * b, see __mul__() __rmul__()
outer product use a @ b, see __matmul__()
-use super constructor
-use super __iter__
-use super __setitem__
->>> v = vector ([ 1 , 2 , 3 , 4 , 5 ])
->>> v [ 3 : 5 ] = [ 1 , 2 ]
+
+__iter__
+
+
>>> [ i * 2 for i in vector ([ 1 , 2 , 3 ])]
+[2, 4, 6]
+
+
+
+__setitem__
+
+
>>> v = vector ([ 1 , 2 , 3 , 4 , 5 ])
+>>> v [ 3 : 5 ] = [ 1 , 2 ]
>>> print ( v )
[1, 2, 3, 1, 2]
>>> isinstance ( v , vector )
True
-
use super __lt__(a, b)
-
use super __le__(a, b)
-
use super __eq__(a, b)
-
>>> v = vector ([ 1 , 2 , 3 , 1 , 2 ])
->>> v2 = vector ([ 1 , 2 , 3 , 1 , 2 ])
->>> v == v2
+
+__eq__(a, b)
+
+
>>> vector ([ 1 , 2 , 3 , 1 , 2 ]) == vector ([ 1 , 2 , 3 , 1 , 2 ])
+True
+>>> vector ([ 1 , 2 , 3 , 1 , 2 ]) == vector ([ 1 , 2 , 3 , 2 , 1 ])
+False
+
+
+
+__ne__(a, b)
+
+
>>> vector ([ 1 , 2 , 3 , 1 , 2 ]) != vector ([ 1 , 2 , 3 , 1 , 2 ])
+False
+>>> vector ([ 1 , 2 , 3 , 1 , 2 ]) != vector ([ 1 , 2 , 3 , 2 , 1 ])
True
-
use super __ne__(a, b)
-
use super __ge__(a, b)
-
use super __gt__(a, b)
-
use super __contains__
-
>>> 2 in vector ([ 1 , 2 , 3 ])
+
+__contains__
+
+
>>> 2 in vector ([ 1 , 2 , 3 ])
True
-
__isub__
-
>>> v = vector ([ 1 , 2 , 3 ])
->>> v -= vector ([ 3 , 3 , 3 ])
+
+__isub__
+
+
>>> v = vector ([ 1 , 2 , 3 ])
+>>> v -= vector ([ 3 , 3 , 3 ])
>>> print ( v )
[-2, -1, 0]
-
__imul__
-
>>> v = vector ([ 1 , 2 , 3 ])
->>> v *= vector ([ 3 , 3 , 3 ])
+
+__imul__
+
+
>>> v = vector ([ 1 , 2 , 3 ])
+>>> v *= vector ([ 3 , 3 , 3 ])
>>> print ( v )
18
-
__imatmul__
-
>>> m = vector ([ 1 , 2 , 3 ])
->>> m *= vector ([ 3 , 3 , 3 ])
+
+__imatmul__
+
+
>>> m = vector ([ 1 , 2 , 3 ])
+>>> m *= vector ([ 3 , 3 , 3 ])
>>> print ( v )
[[3, 3, 3], [6, 6, 6], [9, 9, 9]]
+
+
+__abs__( ) [source]
+Magnitude / norm of a vector
+
+\[b = |\mathbf{a}| = \sqrt{\sum a_i^2} =
+\sqrt{\mathbf{a} \cdot \mathbf{a}}\]
+
+Example
+
+>>> v = vector ([ 3 , 4 ])
+>>> abs ( v )
+5.0
+
+
+
+
+
+__add__( other ) [source]
+a + b (new object)
+
+\[\mathbf{c} = \mathbf{a} + \mathbf{b}\]
+
+Example
+
+>>> v = vector ([ 1 , 2 , 3 ]) + vector ([ 1 , 2 , 3 ])
+>>> print ( v )
+[2, 4, 6]
+
+
+
+
+
+__ge__( other ) [source]
+Test if this object is greater (larger) than or equal the
+other object.
+
+\[|\mathbf{a}| \ge |\mathbf{b}|\]
+
+Example
+
+>>> vector ([ 1 , 2 , 3 ]) >= vector ([ 3 , 2 , 1 ])
+True
+>>> vector ([ 1 , 2 , 3 ]) >= vector ([ 4 , 2 , 1 ])
+False
+
+
+
+
+
+__getitem__( index ) [source]
+For index return value, for range return new vector object.
+
+Example
+
+>>> v = vector ([ 1 , 2 , 3 , 4 , 5 ])
+>>> v [ 1 : 3 ]
+[2, 3]
+>>> v = vector ([ 1 , 2 , 3 , 4 , 5 ])
+>>> v [ 3 ]
+4
+
+
+
+
+
+__gt__( other ) [source]
+Test if this object is greater (larger) than the other
+object.
+
+\[|\mathbf{a}| \gt |\mathbf{b}|\]
+
+Example
+
+>>> vector ([ 1 , 2 , 3 ]) > vector ([ 3 , 2 , 1 ])
+False
+>>> vector ([ 1 , 2 , 3 ]) > vector ([ 2 , 2 , 1 ])
+True
+
+
+
+
+
+__iadd__( other ) [source]
+a += b (new object)
+
+Example
+
+>>> v = vector ([ 1 , 2 , 3 ])
+>>> v += vector ([ 3 , 3 , 3 ])
+>>> print ( v )
+[4, 5, 6]
+
+
+
+
+
+__le__( other ) [source]
+Test if this object is lower (smaller) than or equal the
+other object.
+
+\[|\mathbf{a}| \le |\mathbf{b}|\]
+
+Example
+
+>>> vector ([ 3 , 2 , 1 ]) <= vector ([ 1 , 2 , 3 ])
+True
+>>> vector ([ 3 , 2 , 1 ]) <= vector ([ 1 , 2 , 2 ])
+False
+
+
+
+
+
+__lt__( other ) [source]
+Test if this object is lower (smaller) than the other object.
+
+\[|\mathbf{a}| \lt |\mathbf{b}|\]
+
+Example
+
+>>> vector ([ 3 , 2 , 1 ]) < vector ([ 1 , 2 , 3 ])
+False
+>>> vector ([ 3 , 2 , 1 ]) < vector ([ 1 , 2 , 4 ])
+True
+
+
+
+
+
+__matmul__( other ) [source]
+Outer product a @ b (new object)
+
+\[\begin{split}\mathbf{c} = \mathbf{a} \otimes \mathbf{b}
+=
+\begin{pmatrix}
+ a_{1}\\
+ a_{2}\\
+ a_{3}
+\end{pmatrix}
+\otimes
+\begin{pmatrix}
+ b_{1}\\
+ b_{2}\\
+ b_{3}
+\end{pmatrix}
+=
+\begin{pmatrix}
+ a_{1}b_{1}&a_{1}b_{2}&a_{1}b_{3}\\
+ a_{2}b_{1}&a_{2}b_{2}&a_{2}b_{3}\\
+ a_{3}b_{1}&a_{3}b_{2}&a_{3}b_{3}
+\end{pmatrix}\end{split}\]
+
+Example
+
+>>> m = vector ([ 1 , 2 , 3 ]) @ vector ([ 1 , 2 , 4 ])
+>>> print ( m )
+[[1, 2, 4], [2, 4, 8], [3, 6, 12]]
+
+
+
+
+
+__mul__( other ) [source]
+Scalar multiplication, dot product (inner product) or
+vector-matrix multiplication. (new object)
+
+
+
+\[\begin{split}\mathbf{c} &= \mathbf{a} \cdot b \\
+\mathbf{c} &= \mathbf{a} \cdot \mathbf{b} \\
+\mathbf{c} &= \mathbf{a} \cdot \mathbf{B}\end{split}\]
+
+
Note
+
No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).
+
+Example
+
+>>> v = vector ([ 1 , 2 , 3 , 4 , 5 ]) * 3
+>>> print ( v )
+[3, 6, 9, 12, 15]
+>>> v = vector ([ 1 , 2 , 3 , 4 , 5 ]) * 3.
+>>> print ( v )
+[3.0, 6.0, 9.0, 12.0, 15.0]
+>>> s = vector ([ 1 , 2 , 3 ]) * vector ([ 1 , 2 , 3 ])
+>>> print ( s )
+14
+
+
+
+
+
+__neg__( ) [source]
+- a (new object)
+
+\[\mathbf{b} = -\mathbf{a}\]
+
+
+
+
+__pos__( ) [source]
++ a (new object)
+
+\[\mathbf{b} = +\mathbf{a}\]
+
+
+
+
+__repr__( ) [source]
+Return repr(self).
+
+
+
+
+__rmul__( other ) [source]
+Scalar multiplication, dot product (inner product) or
+matrix-vector multiplication. (new object)
+
+
+
+\[\begin{split}\mathbf{c} &= a \cdot \mathbf{b} \\
+\mathbf{c} &= \mathbf{a} \cdot \mathbf{b} \\
+\mathbf{c} &= \mathbf{A} \cdot \mathbf{b}\end{split}\]
+
+
Note
+
No size checking will be conducted, therefore no exceptions
+for wrong usage (result will be nonsense).
+
+Example
+
+>>> v = 3 * vector ([ 1 , 2 , 3 , 4 , 5 ])
+>>> print ( v )
+[3, 6, 9, 12, 15]
+>>> v = 3. * vector ([ 1 , 2 , 3 , 4 , 5 ])
+>>> print ( v )
+[3.0, 6.0, 9.0, 12.0, 15.0]
+
+
+
+
+
+__str__( ) [source]
+Return str(self).
+
+
+
+
+__sub__( other ) [source]
+a - b (new object)
+
+\[\mathbf{c} = \mathbf{a} - \mathbf{b}\]
+
+Example
+
+>>> v = vector ([ 1 , 2 , 3 ]) - vector ([ 1 , 2 , 3 ])
+>>> print ( v )
+[0, 0, 0]
+
+
+
static abs( a ) [source]
@@ -370,9 +811,9 @@ it should be.
ch_cs( cs ) [source]
-Transform this vector from its defined coordinate system to a
-new coordinate system, defined by the given coordinate system (u,
-v and w direction vectors).
+Transform this vector from its defined coordinate system to
+a new coordinate system, defined by the given coordinate system
+(u, v and w direction vectors).
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
@@ -401,7 +842,7 @@ v and w direction vectors).
c is orthogonal to both a and b.
The direction of c can be found with the right-hand rule.
-\[\vec{c} = \vec{a} \times \vec{b}\]
+\[\mathbf{c} = \mathbf{a} \times \mathbf{b}\]
@@ -444,10 +885,10 @@ columns filled with v.
-\[\vec{e}_a = \frac{\vec{a}}{|\vec{a}|}\]
+\[\mathbf{\hat{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}\]
See also
-
norm()
+
__abs__()
@@ -473,8 +914,8 @@ columns filled with ones.
static random( shape , lmin=0.0 , lmax=1.0 ) [source]
-Returns a random vector of length n or matrix of size m rows, n
-columns filled with random numbers.
+Returns a random vector of length n or matrix of size m rows,
+n columns filled with random numbers.
Example
Scaling
uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
-centered at the origin will have their centers move. To avoid this,
-either scale the object when it’s located at the origin, or
-perform a translation afterwards to move the object back to where
-it should be.
+centered at the origin will have their centers move. To avoid
+this, either scale the object when it’s located at the origin,
+or perform a translation afterwards to move the object back to
+where it should be.
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
@@ -578,11 +1019,6 @@ it should be.
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]
-
-
-xyz( ) [source]
-
-
static zeros( length ) [source]
@@ -637,7 +1073,7 @@ columns filled with zeros.
Documentation overview
pylib
+"""
+from pylib.geometry import World, Hexahedron
+from pylib.geometry_plot_pylab import cad_wireframe
+
+def geometry():
+ w = World()
+ for i in range(3):
+ for j in range(3):
+ for k in range(3):
+ w.add(Hexahedron().scale(0.8).translate(-2+2*i, -2+2*j, -2+2*k))
+ return w
+
+
+if __name__ == "__main__":
+ w = geometry()
+ #print(w.bounding_box())
+ #print(*w)
+ #print(w.wireframes_xyz())
+ cad_wireframe(w)
diff --git a/examples/geometry_lines_circles.py b/examples/geometry_lines_circles.py
new file mode 100644
index 0000000..a926fd2
--- /dev/null
+++ b/examples/geometry_lines_circles.py
@@ -0,0 +1,41 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Example geometry of lines and circles.
+
+:Date: 2019-12-23
+
+.. module:: geometry_pyramidal_frustum
+ :platform: *nix, Windows
+ :synopsis: Example geometry of lines and circles.
+
+.. moduleauthor:: Daniel Weschke
+"""
+import math
+from pylib.geometry import World, Point, Line, Circle
+from pylib.geometry_plot_pylab import cad_wireframe, wireframe3d
+
+def geometry():
+ w = World()
+
+ p0 = Point(0, 0, 0)
+ p = Point(1, 1, 1)
+
+ # add Lines to the Word
+ theta = math.pi/4
+ w.add(*[Line(p0, p.rotate_x(theta/5)) for i in range(30)])
+ w.add(*[Line(p0, p.rotate_x(theta/5)).translate(.1*i, 0, 0) for i in range(30)])
+
+ # add Circles to the Word
+ c1 = Circle()
+ c2 = Circle(2)
+ c3 = Circle(n=18).scale(3).rotate_x(math.pi/4)
+ w.add(c1, c2, c3)
+
+ return w
+
+
+if __name__ == "__main__":
+ w = geometry()
+ print(*w)
+ wireframe3d(w)
+ cad_wireframe(w, False)
diff --git a/examples/geometry_pyramidal_frustum.py b/examples/geometry_pyramidal_frustum.py
new file mode 100644
index 0000000..876659d
--- /dev/null
+++ b/examples/geometry_pyramidal_frustum.py
@@ -0,0 +1,40 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Example geometry of a pyramidal frustum.
+
+:Date: 2019-12-23
+
+.. module:: geometry_pyramidal_frustum
+ :platform: *nix, Windows
+ :synopsis: Example geometry of a pyramidal frustum.
+
+.. moduleauthor:: Daniel Weschke
+"""
+from pylib.geometry import World, Point, Polygon, Hexahedron
+from pylib.geometry_plot_pylab import cad_wireframe
+
+def geometry():
+ w = World()
+ p0 = Point()
+ p1 = Point(1.00, 0, 0)
+ p2 = Point(1.00, 1, 0)
+ p3 = Point(0.00, 1, 0)
+ p4 = Point(0.25, 0.25, 1)
+ p5 = Point(0.75, 0.25, 1)
+ p6 = Point(0.75, 0.75, 1)
+ p7 = Point(0.25, 0.75, 1)
+ pg0 = Polygon(p0, p1, p2, p3)
+ pg1 = Polygon(p4, p5, p6, p7)
+ pg2 = Polygon(p0, p1, p5, p4)
+ pg3 = Polygon(p2, p3, p7, p6)
+ w.add(pg0, pg1, pg2, pg3)
+ h = Hexahedron()
+ w.add(h)
+ return w
+
+
+if __name__ == "__main__":
+ w = geometry()
+ print(*w)
+ print(w.wireframes_xyz())
+ cad_wireframe(w)
diff --git a/pylib/data.py b/pylib/data.py
index 7f3e694..80a4d3d 100644
--- a/pylib/data.py
+++ b/pylib/data.py
@@ -12,6 +12,36 @@
"""
import math
import pickle
+import collections
+
+def issequence(obj):
+ """
+ True for tuple, list, str
+ False for int, dict, set
+
+ :Example:
+
+ >>> issequence(())
+ True
+ >>> issequence((3, ))
+ True
+ >>> issequence([])
+ True
+ >>> issequence([1])
+ True
+ >>> issequence([1, 2])
+ True
+ >>> issequence('')
+ True
+
+ >>> issequence((3))
+ False
+ >>> issequence({})
+ False
+ >>> issequence(set())
+ False
+ """
+ return isinstance(obj, collections.abc.Sequence)
def read(file_name, x_column, y_column, default=None, verbose=False):
"""Read ascii data file.
diff --git a/pylib/function.py b/pylib/function.py
index 95e6a8d..31e65aa 100644
--- a/pylib/function.py
+++ b/pylib/function.py
@@ -200,7 +200,7 @@ def hypotrochoid(R, r, d):
>>> x, y, theta_end = hyotrochoid(20, 6, 6)
.. seealso::
- :meth:`mathematics.lcm`
+ :meth:`pylib.mathematics.lcm`
"""
x = lambda theta: (R-r)*math.cos(theta) + d*math.cos((R-r)/r * theta)
y = lambda theta: (R-r)*math.sin(theta) - d*math.sin((R-r)/r * theta)
@@ -377,7 +377,7 @@ def to_str(f, x=None, x_0=0, x_1=1, t=None, h=10, w=80, density=1, char_set="lin
.. seealso::
- :meth:`pylib.function.transformation`
+ :meth:`transformation`
"""
# scale function to used chars and dots/pixel in y direction (4 for braille characters): from [0, 1] to [0, chars*4-1]
# negate the function because the y axis is pointing downwards: from [0, 1] to [-1, 0] or from [0, chars*4-1] to [-(chars*4-1), 0]
@@ -402,7 +402,7 @@ def to_str(f, x=None, x_0=0, x_1=1, t=None, h=10, w=80, density=1, char_set="lin
#frame = canvas.frame(min_x=a*pixel_per_char, min_y=1, max_x=b*pixel_per_char, max_y=21)
frame = canvas.frame()
elif char_set in ["histogram", "block"]:
- import drawblock
+ from .drawblock import histogram
pixels_horizontal = 1
pixels_vertical = 8
@@ -412,6 +412,6 @@ def to_str(f, x=None, x_0=0, x_1=1, t=None, h=10, w=80, density=1, char_set="lin
density = min(density, 1) # density max 1!
x = seq(x_0*window_factor, x_1*window_factor, 1/pixels_horizontal/density)
f = [f(xi, t) for xi in x]
- frame = drawblock.histogram(f, x)
+ frame = histogram(f, x)
return frame
diff --git a/pylib/geometry.py b/pylib/geometry.py
index e14df30..53c97a0 100644
--- a/pylib/geometry.py
+++ b/pylib/geometry.py
@@ -1,6 +1,6 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
-"""2D geometry objects.
+"""Geometry objects.
:Date: 2019-12-21
@@ -9,26 +9,37 @@
:synopsis: Geometry objects.
.. moduleauthor:: Daniel Weschke
+
+Affine transforms
+-----------------
+
+Functions in augmented space, in homogenous coordinates.
+Points are augment to 4 dimensions, by adding a dummy coordinate.
+For points the dummy coordinate is always normalized to 1.
+With homogenous coordinates translation of points is repesentable
+as a linear transformation.
"""
import math
import copy
-from pylib.mathematics import vector, matrix
+from .mathematics import vector, matrix
class Direction(vector):
"""Direction in local coordinate system"""
def __init__(self, x=1, y=0, z=0):
super().__init__([x, y, z, 0])
- def __str__(self):
- return str(self.xyz())
-
class Point(vector):
"""Point in local coordinate system"""
def __init__(self, x=0, y=0, z=0):
super().__init__([x, y, z, 1])
- def __str__(self):
- return str(self.xyz())
+ # TODO
+ def projection(self):
+ """Orthographic projection to the xy-plane
+ """
+ # P = matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
+ #return (P*self)[:2]
+ return self[:2]
class CS(matrix):
"""Coordinate system
@@ -36,9 +47,6 @@ class CS(matrix):
def __init__(self, x=[1, 0, 0], y=[0, 1, 0], z=[0, 0, 1]):
super().__init__([[*x, 0], [*y, 0], [*z, 0], [0, 0, 0, 1]])
- def __str__(self):
- return '[' + ', '.join([str(i) for i in self.get_coordinates()]) + ']'
-
@staticmethod
def x90():
return CS((1, 0, 0), (0, 0, -1), (0, 1, 0))
@@ -59,7 +67,133 @@ class CS(matrix):
"""Get coordinates in 3d space"""
return self[:3,:3]
-class World():
+# TODO: Wireframe(list) or Wireframe(matrix) ?
+# list of Points
+class Wireframe:
+ """Open and closed wireframe object in local coordinate system
+
+ This class create its own points (copy).
+ """
+ def __init__(self, *points, closed=False):
+ self._points = [copy.copy(i) for i in points]
+ self.closed = closed
+
+ def __str__(self):
+ return '[' + ', '.join([str(point) for point in self._points]) + ']'
+
+ def __iter__(self):
+ """Returns the Iterator object"""
+ return iter(self.points())
+
+ def points(self):
+ """Get coordinates in 3d space"""
+ result = [i for i in self._points]
+ return result if not self.closed else result + [result[0]]
+
+ def xy(self):
+ """Get coordinates in 3d space"""
+ return list(zip(*[i[:2] for i in self.points()]))
+
+ def xyz(self):
+ """Get coordinates in 3d space"""
+ return list(zip(*[i[:3] for i in self.points()]))
+
+ def rotate_x(self, theta):
+ self._points = [point.rotate_x(theta) for point in self._points]
+ return self
+
+ def rotate_y(self, theta):
+ self._points = [point.rotate_y(theta) for point in self._points]
+ return self
+
+ def rotate_z(self, theta):
+ self._points = [point.rotate_z(theta) for point in self._points]
+ return self
+
+ def translate(self, tx, ty, tz):
+ self._points = [point.translate(tx, ty, tz) for
+ point in self._points]
+ return self
+
+ def scale(self, sx, sy=None, sz=None):
+ # if not sy is not suitable because 0 is also false
+ if sy is None:
+ sy = sx
+ sz = sx
+ self._points = [point.scale(sx, sy, sz) for
+ point in self._points]
+ return self
+
+ def ch_cs(self, cs):
+ self._points = [point.ch_cs(cs) for point in self._points]
+ return self
+
+class Line(Wireframe):
+ """Line a open wireframe object in local coordinate system"""
+ def __init__(self, point1=Point(-1, 0, 0), point2=Point(1, 0, 0)):
+ super().__init__(point1, point2)
+
+class Polygon(Wireframe):
+ """Polygon as closed wireframe object in local coordinate system"""
+ def __init__(self, *points):
+ super().__init__(*points, closed=True)
+
+class Circle(Polygon):
+ """Circle a closed wireframe object in local coordinate system"""
+ def __init__(self, radius=1, n=10):
+ points = []
+ for i in range(n):
+ x = radius * math.cos(i*2*math.pi/n)
+ y = radius * math.sin(i*2*math.pi/n)
+ points.append(Point(x, y, 0))
+ super().__init__(*points)
+
+class Solid:
+ """Solid object in local coordinate system
+
+ This class lists Wireframe objects.
+ The Wireframe class create its own points (copy).
+ """
+ def __init__(self, *wireframes):
+ self._wireframes = wireframes
+
+ def wireframes(self):
+ return self._wireframes
+
+ def translate(self, tx, ty, tz):
+ self._wireframes = [wireframe.translate(tx, ty, tz) for
+ wireframe in self._wireframes]
+ return self
+
+ def scale(self, sx, sy=None, sz=None):
+ # if not sy is not suitable because 0 is also false
+ if sy is None:
+ sy = sx
+ sz = sx
+ self._wireframes = [wireframe.scale(sx, sy, sz) for
+ wireframe in self._wireframes]
+ return self
+
+ def ch_cs(self, cs):
+ self._wireframes = [wireframe.ch_cs(cs) for
+ wireframe in self._wireframes]
+ return self
+
+class Hexahedron(Solid):
+ """Line a open wireframe object in local coordinate system"""
+ def __init__(self,
+ point1=Point(-1, -1, -1), point2=Point(1, -1, -1),
+ point3=Point(1, 1, -1), point4=Point(-1, 1, -1),
+ point5=Point(-1, -1, 1), point6=Point(1, -1, 1),
+ point7=Point(1, 1, 1), point8=Point(-1, 1, 1)):
+ super().__init__(
+ Polygon(point1, point2, point3, point4),
+ Polygon(point5, point6, point7, point8),
+ Polygon(point1, point2, point6, point5),
+ Polygon(point3, point4, point8, point7)
+ )
+
+class World:
"""World-space with world-space coordinates
"""
def __init__(self):
@@ -72,7 +206,8 @@ class World():
return iter(self.objects())
def _store_init(self):
- """Initialize or reset calculated values, because a new object was added.
+ """Initialize or reset calculated values, because a new object
+ was added.
"""
self._bb = None
self._sd = None
@@ -106,6 +241,33 @@ class World():
self._cs.scale(sx, sy, sz)
return self
+ def wireframes(self):
+ result = []
+ for i in self.objects():
+ if isinstance(i, Wireframe):
+ result.append(i.points())
+ elif isinstance(i, Solid):
+ [result.append(j.points()) for j in i.wireframes()]
+ return result
+
+ def wireframes_xy(self):
+ result = []
+ for i in self.objects():
+ if isinstance(i, Wireframe):
+ result.append(i.xy())
+ elif isinstance(i, Solid):
+ [result.append(j.xy()) for j in i.wireframes()]
+ return result
+
+ def wireframes_xyz(self):
+ result = []
+ for i in self.objects():
+ if isinstance(i, Wireframe):
+ result.append(i.xyz())
+ elif isinstance(i, Solid):
+ [result.append(j.xyz()) for j in i.wireframes()]
+ return result
+
def objects(self):
return [copy.deepcopy(i).ch_cs(self._cs) for i in self._objects]
@@ -124,10 +286,9 @@ class World():
xmax = -math.inf
ymax = -math.inf
zmax = -math.inf
- for i in self._objects:
- xi, yi, zi = map(min, i.xyz())
- xs, ys, zs = map(max, i.xyz())
- #xmax = x if x > xmax: xmax = x
+ for i in self.wireframes_xyz():
+ xi, yi, zi = map(min, i)
+ xs, ys, zs = map(max, i)
xmin = xi if xi < xmin else xmin
ymin = yi if yi < ymin else ymin
zmin = zi if zi < zmin else zmin
@@ -148,78 +309,8 @@ class World():
def center(self):
bb = self.bounding_box()
- self.ch_cs([[1,0,0,-(bb[1]-bb[0])/2],[0,1,0,-(bb[3]-bb[2])/2],[0,0,1,-(bb[5]-bb[4])/2],[0,0,0,1]])
+ self.ch_cs([[1, 0, 0, -(bb[0]+bb[1])/2],
+ [0, 1, 0, -(bb[2]+bb[3])/2],
+ [0, 0, 1, -(bb[4]+bb[5])/2],
+ [0, 0, 0, 1]])
return self
-
-# TODO: Wireframe(list) or Wireframe(matrix) ?
-# list of Points
-class Wireframe():
- """Open and closed wireframe object in local coordinate system
-
- This class create its own points (copy).
- """
- def __init__(self, *points, closed=False):
- self._points = [copy.copy(i) for i in points]
- self.closed = closed
-
- def __str__(self):
- return '[' + ', '.join([str(point) for point in self._points]) + ']'
-
- def __iter__(self):
- """Returns the Iterator object"""
- return iter(self.points())
-
- def points(self):
- """Get coordinates in 3d space"""
- result = [i for i in self._points]
- return result if not self.closed else result + [result[0]]
-
- def xyz(self):
- return zip(*[i.xyz() for i in self.points()])
-
- def rotate_x(self, theta):
- self._points = [point.rotate_x(theta) for point in self._points]
- return self
-
- def rotate_y(self, theta):
- self._points = [point.rotate_y(theta) for point in self._points]
- return self
-
- def rotate_z(self, theta):
- self._points = [point.rotate_z(theta) for point in self._points]
- return self
-
- def translate(self, tx, ty, tz):
- self._points = [point.translate(tx, ty, tz) for point in self._points]
- return self
-
- def scale(self, sx, sy=None, sz=None):
- if not sy:
- sy = sx
- sz = sx
- self._points = [point.scale(sx, sy, sz) for point in self._points]
- return self
-
- def ch_cs(self, cs):
- self._points = [point.ch_cs(cs) for point in self._points]
- return self
-
-class Line(Wireframe):
- """Line a open wireframe object in local coordinate system"""
- def __init__(self, point1=Point(-1, 0, 0), point2=Point(1, 0, 0)):
- super().__init__(point1, point2)
-
-class Polygon(Wireframe):
- """Polygon as closed wireframe object in local coordinate system"""
- def __init__(self, *points):
- super().__init__(*points, closed=True)
-
-class Circle(Polygon):
- """Circle a closed wireframe object in local coordinate system"""
- def __init__(self, radius=1, n=10):
- points = []
- for i in range(n):
- x = radius * math.sin(i*2*math.pi/n)
- y = radius * math.cos(i*2*math.pi/n)
- points.append(Point(x, y, 0))
- super().__init__(*points)
diff --git a/pylib/geometry2d_plot.py b/pylib/geometry2d_plot.py
index 7f5aa65..c123e1d 100644
--- a/pylib/geometry2d_plot.py
+++ b/pylib/geometry2d_plot.py
@@ -11,7 +11,7 @@
.. moduleauthor:: Daniel Weschke
"""
import pylab
-from geometry2d import (
+from .geometry2d import (
distance, angle, line, interpolate_hermite, rotate_xy, translate_xy
)
diff --git a/pylib/geometry_plot.py b/pylib/geometry_plot.py
new file mode 100644
index 0000000..9b68819
--- /dev/null
+++ b/pylib/geometry_plot.py
@@ -0,0 +1,17 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Geometry plotter using matplotlib (pylab).
+
+:Date: 2019-12-23
+
+.. module:: geometry_plot
+ :platform: *nix, Windows
+ :synopsis: Geometry plotting.
+
+.. moduleauthor:: Daniel Weschke
+"""
+
+backend = 'pylab'
+
+if backend == 'pylab':
+ from .geometry_plot_pylab import cad_wireframe, wireframe3d
diff --git a/pylib/geometry_plot_pylab.py b/pylib/geometry_plot_pylab.py
new file mode 100644
index 0000000..9c0f92c
--- /dev/null
+++ b/pylib/geometry_plot_pylab.py
@@ -0,0 +1,243 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Geometry plotter using pylab (matplotlib).
+
+:Date: 2019-12-23
+
+.. module:: geometry_plot_pylab
+ :platform: *nix, Windows
+ :synopsis: Geometry plotting (pylab).
+
+.. moduleauthor:: Daniel Weschke
+"""
+import math
+# This import registers the 3D projection, but is otherwise unused.
+from mpl_toolkits.mplot3d import Axes3D
+assert Axes3D # silence pyflakes
+import pylab
+pylab.style.use('dark_background')
+pylab.rcParams['text.color'] = 'grey' # lightgrey
+pylab.rcParams['axes.edgecolor'] = 'grey' # lightgrey
+pylab.rcParams['grid.color'] = 'grey' # lightgrey
+pylab.rcParams['xtick.color'] = 'grey' # lightgrey
+pylab.rcParams['ytick.color'] = 'grey' # lightgrey
+pylab.rcParams['axes3d.grid'] = False
+# default for dark_background cycler(
+# 'color', ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',
+# '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf'])
+pylab.rcParams['axes.prop_cycle'] = pylab.cycler(
+ "color", ['#3498DB', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd',
+ '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf'])
+
+# remove f for fullscreen toggle, default ['f', 'ctrl+f']
+pylab.rcParams['keymap.fullscreen'] = ['ctrl+f']
+# remove L for log/lin toggle, default ['k', 'L']
+pylab.rcParams['keymap.xscale'] = ['k']
+# remove l for log/lin toggle, default ['l']
+pylab.rcParams['keymap.yscale'] = []
+
+from pylab import mean
+from .geometry import CS
+
+# type of ax
+# - matplotlib.axes._subplots.Axes3DSubplot)
+# - matplotlib.axes.Axes
+# - pylab.Axes
+
+def set_aspect_equal(ax):
+ '''Make axes of 3D plot have equal scale so that spheres appear as
+ spheres, cubes as cubes, etc.. This is one possible solution to
+ Matplotlib's ax.set_aspect('equal') and ax.axis('equal') not
+ working for 3D.
+
+ :param ax: a pylab axis
+ :type ax: pylab.Axes
+
+ Source: https://stackoverflow.com/a/35126679
+ '''
+ if ax.name == '3d':
+
+ xlim = ax.get_xlim3d()
+ ylim = ax.get_ylim3d()
+ zlim = ax.get_zlim3d()
+
+ xmean = mean(xlim)
+ ymean = mean(ylim)
+ zmean = mean(zlim)
+
+ plot_radius = max([abs(lim - mean_)
+ for lims, mean_ in ((xlim, xmean),
+ (ylim, ymean),
+ (zlim, zmean))
+ for lim in lims])
+
+ ax.set_xlim3d([xmean - plot_radius, xmean + plot_radius])
+ ax.set_ylim3d([ymean - plot_radius, ymean + plot_radius])
+ ax.set_zlim3d([zmean - plot_radius, zmean + plot_radius])
+ else:
+ ax.axis('equal')
+
+def plot_post(ax):
+ if isinstance(ax, pylab.Axes):
+ ax = [ax]
+ for axi in ax:
+ if axi.name == '3d':
+ #axi.w_xaxis.set_pane_color((0, 0, 0, 0))
+ #axi.w_yaxis.set_pane_color((0, 0, 0, 0))
+ #axi.w_zaxis.set_pane_color((0, 0, 0, 0))
+ axi.w_xaxis.pane.fill = False
+ axi.w_yaxis.pane.fill = False
+ axi.w_zaxis.pane.fill = False
+ set_aspect_equal(axi)
+
+def wireframe3d(world):
+ fig = pylab.figure()
+ ax = fig.add_subplot(111, projection='3d')
+ [ax.plot(*i, 'C0') for i in world.wireframes_xyz()]
+ plot_post(ax)
+
+def cad_wireframe(world, centering=True):
+ """
+ Graphical projections
+
+ * Parallel projections
+
+ * Orthographic
+
+ * Multiview
+
+ * \* First-angle
+ * Third-angle
+ * Plan Elevation
+
+ * Axonometric
+
+ * \* Isometric
+ * Dimetric
+ * Trimetri
+
+ * Oblique
+
+ * Carbinet
+ * Cavalier
+ * Military
+ * Top-down
+
+ * Perspective projections
+
+ * 1-point
+ * 2-point
+ * 3-point
+ * Curvilinear
+
+ """
+ if centering:
+ world.center()
+
+ fig = pylab.figure('geometry-cad')
+ fig.clf()
+ ax = fig.add_subplot(111)
+
+ pylab.axis('off')
+ pylab.subplots_adjust(left=0, right=1, top=1, bottom=0)
+
+ lps = [ax.plot(*i, 'C0')[0] for i in world.wireframes_xy()]
+
+ plot_post(ax)
+
+ def press(event, world, lps):
+ #print('key pressed:', event.key)
+ #sys.stdout.flush()
+ if event.key in [
+ 'left', 'right', 'up', 'down',
+ 'f', 't', 'b', 'l', 'r', 'i', 'd',
+ 'shift+left', 'shift+right', 'shift+up', 'shift+down',
+ 'ctrl+up', 'ctrl+down', 'ctrl+left', 'ctrl+right']:
+ d = world.space_diagonal()
+ if event.key == 'left':
+ world.rotate_y(-math.pi/180*10)
+ elif event.key == 'right':
+ world.rotate_y(+math.pi/180*10)
+ elif event.key == 'up':
+ world.rotate_x(-math.pi/180*10)
+ elif event.key == 'down':
+ world.rotate_x(+math.pi/180*10)
+ elif event.key == 'f':
+ world.cs(CS())
+ if centering:
+ world.center()
+ elif event.key == 't':
+ world.cs(CS.x90())
+ if centering:
+ world.center()
+ elif event.key == 'b':
+ world.cs(CS.xm90())
+ if centering:
+ world.center()
+ elif event.key == 'l':
+ world.cs(CS.y90())
+ if centering:
+ world.center()
+ elif event.key == 'r':
+ world.cs(CS.ym90())
+ if centering:
+ world.center()
+ elif event.key == 'i':
+ #theta_y = -math.pi/2/3
+ #theta_x = math.pi/2/3
+ theta_y = -math.pi/2/2
+ theta_x = math.asin(math.tan(math.pi/2/3))
+ world.cs(CS().rotate_y(theta_y).rotate_x(theta_x))
+ if centering:
+ world.center()
+ elif event.key == 'd':
+ #theta_x = math.asin(math.tan(math.pi/2/3/2))
+ theta_y = -math.pi/2/2
+ theta_x = math.atan(1/2)
+ world.cs(CS().rotate_y(theta_y).rotate_x(theta_x))
+ if centering:
+ world.center()
+ elif event.key == 'shift+left':
+ world.translate(-0.1*d, 0, 0)
+ elif event.key == 'shift+right':
+ world.translate(0.1*d, 0, 0)
+ elif event.key == 'shift+up':
+ world.translate(0, 0.1*d, 0)
+ elif event.key == 'shift+down':
+ world.translate(0, -0.1*d, 0)
+ elif event.key == 'ctrl+left':
+ world.rotate_z(+math.pi/180*10)
+ elif event.key == 'ctrl+right':
+ world.rotate_z(-math.pi/180*10)
+ elif event.key == 'ctrl+up':
+ world.scale(1.1)
+ elif event.key == 'ctrl+down':
+ world.scale(0.9)
+ for i, j in zip(lps, world.wireframes_xy()):
+ i.set_data(j)
+ fig.canvas.draw()
+
+ def onresize(event, w):
+ r = 2 * w.space_diagonal()/2
+ pylab.xlim((-r, r))
+ pylab.ylim((-r, r))
+
+ fig.canvas.mpl_connect('key_press_event',
+ lambda event: press(event, world, lps))
+ fig.canvas.mpl_connect('resize_event',
+ lambda event: onresize(event, world))
+
+ pylab.text(
+ 0+.01, 1-.015,
+ 'rotate: left, right, up, down, ctrl+left, ctrl+right\n' +
+ 'pan: shift+left, shift+right, shift+up, shift+down\n' +
+ 'zoom: ctrl+up, ctrl+down\n' +
+ 'view: f (front), l (left), r (right), t (top), b (bottom)\n' +
+ ' i (isometric), d (dimetric)',
+ horizontalalignment='left',
+ verticalalignment='top',
+ transform=fig.transFigure,
+ bbox=dict(facecolor='black', alpha=0.5),
+ family='monospace'
+ )
+ pylab.show()
diff --git a/pylib/mathematics.py b/pylib/mathematics.py
index a2298d3..11d2803 100644
--- a/pylib/mathematics.py
+++ b/pylib/mathematics.py
@@ -21,64 +21,63 @@ def lcm(a, b):
class vector(list):
"""Use/create vector like lists
- * size -> len(a)
- * abs -> abs(a)
- * dot -> a * b
- * outer -> a @ b
+ * size, length of a vector use len(a)
+ * absolute, magntude, norm of a vector use abs(a), see
+ :meth:`__abs__`
+ * dot product use a * b, see :meth:`__mul__` and :meth:`__rmul__`
+ * outer product use a @ b, see :meth:`__matmul__`
- use super constructor
+ :__iter__:
- use super __iter__
+ >>> [i*2 for i in vector([1, 2, 3])]
+ [2, 4, 6]
- use super __setitem__
+ :__setitem__:
- >>> v = vector([1,2,3,4,5])
- >>> v[3:5] = [1,2]
+ >>> v = vector([1, 2, 3, 4, 5])
+ >>> v[3:5] = [1, 2]
>>> print(v)
[1, 2, 3, 1, 2]
>>> isinstance(v, vector)
True
- use super __lt__(a, b)
+ :__eq__(a, b):
- use super __le__(a, b)
+ >>> vector([1, 2, 3, 1, 2]) == vector([1, 2, 3, 1, 2])
+ True
+ >>> vector([1, 2, 3, 1, 2]) == vector([1, 2, 3, 2, 1])
+ False
- use super __eq__(a, b)
+ :__ne__(a, b):
- >>> v = vector([1,2,3,1,2])
- >>> v2 = vector([1,2,3,1,2])
- >>> v == v2
+ >>> vector([1, 2, 3, 1, 2]) != vector([1, 2, 3, 1, 2])
+ False
+ >>> vector([1, 2, 3, 1, 2]) != vector([1, 2, 3, 2, 1])
True
- use super __ne__(a, b)
+ :__contains__:
- use super __ge__(a, b)
-
- use super __gt__(a, b)
-
- use super __contains__
-
- >>> 2 in vector([1,2,3])
+ >>> 2 in vector([1, 2, 3])
True
- __isub__
+ :__isub__:
- >>> v = vector([1,2,3])
- >>> v -= vector([3,3,3])
+ >>> v = vector([1, 2, 3])
+ >>> v -= vector([3, 3, 3])
>>> print(v)
[-2, -1, 0]
- __imul__
+ :__imul__:
- >>> v = vector([1,2,3])
- >>> v *= vector([3,3,3])
+ >>> v = vector([1, 2, 3])
+ >>> v *= vector([3, 3, 3])
>>> print(v)
18
- __imatmul__
+ :__imatmul__:
- >>> m = vector([1,2,3])
- >>> m *= vector([3,3,3])
+ >>> m = vector([1, 2, 3])
+ >>> m *= vector([3, 3, 3])
>>> print(v)
[[3, 3, 3], [6, 6, 6], [9, 9, 9]]
"""
@@ -101,33 +100,43 @@ class vector(list):
return vector(item) if isinstance(item, list) else item
def __pos__(self):
- """+ a (new object)
+ """\+ a (new object)
+
+ .. math::
+ \mathbf{b} = +\mathbf{a}
"""
return vector([*self])
def __neg__(self):
- """- a (new object)
+ """\- a (new object)
+
+ .. math::
+ \mathbf{b} = -\mathbf{a}
"""
return vector([-i for i in self])
def __add__(self, other):
"""a + b (new object)
+ .. math::
+ \mathbf{c} = \mathbf{a} + \mathbf{b}
+
:Example:
- >>> v = vector([1,2,3]) + vector([1,2,3])
+ >>> v = vector([1, 2, 3]) + vector([1, 2, 3])
>>> print(v)
[2, 4, 6]
"""
return vector([i+j for i, j in zip(self, other)])
+ # overwrite because [1, 2] + [5, 8] = [1, 2, 5, 8]
def __iadd__(self, other):
"""a += b (new object)
:Example:
- >>> v = vector([1,2,3])
- >>> v += vector([3,3,3])
+ >>> v = vector([1, 2, 3])
+ >>> v += vector([3, 3, 3])
>>> print(v)
[4, 5, 6]
"""
@@ -136,9 +145,12 @@ class vector(list):
def __sub__(self, other):
"""a - b (new object)
+ .. math::
+ \mathbf{c} = \mathbf{a} - \mathbf{b}
+
:Example:
- >>> v = vector([1,2,3]) - vector([1,2,3])
+ >>> v = vector([1, 2, 3]) - vector([1, 2, 3])
>>> print(v)
[0, 0, 0]
"""
@@ -146,9 +158,7 @@ class vector(list):
def __mul__(self, other):
r"""Scalar multiplication, dot product (inner product) or
- vector-matrix multiplication.
-
- a * b (new object)
+ vector-matrix multiplication. (new object)
:type other: scalar, vector (or 1d list), matrix (or 2d list)
@@ -158,18 +168,18 @@ class vector(list):
\mathbf{c} &= \mathbf{a} \cdot \mathbf{B}
.. note::
- No size checking will be conducted, therefore no exceptions for
- wrong usage (result will be nonsense).
+ No size checking will be conducted, therefore no exceptions
+ for wrong usage (result will be nonsense).
:Example:
- >>> v = vector([1,2,3,4,5])*3
+ >>> v = vector([1, 2, 3, 4, 5]) * 3
>>> print(v)
[3, 6, 9, 12, 15]
- >>> v = vector([1,2,3,4,5])*3.
+ >>> v = vector([1, 2, 3, 4, 5]) * 3.
>>> print(v)
[3.0, 6.0, 9.0, 12.0, 15.0]
- >>> s = vector([1,2,3])*vector([1,2,3])
+ >>> s = vector([1, 2, 3]) * vector([1, 2, 3])
>>> print(s)
14
@@ -180,15 +190,14 @@ class vector(list):
return sum([i*j for i, j in zip(self, other)])
except:
try: # vector * matrix
- return vector([sum(c*d for c, d in zip(self, b_col)) for b_col in zip(*other)])
+ return vector([sum(c*d for c, d in zip(self, b_col)) for
+ b_col in zip(*other)])
except: # vector * scalar
return vector([i*other for i in self])
def __rmul__(self, other):
r"""Scalar multiplication, dot product (inner product) or
- matrix-vector multiplication.
-
- a * b (new object)
+ matrix-vector multiplication. (new object)
:type other: scalar (or 1d list and 2d list)
@@ -198,24 +207,24 @@ class vector(list):
\mathbf{c} &= \mathbf{A} \cdot \mathbf{b}
.. note::
- No size checking will be conducted, therefore no exceptions for
- wrong usage (result will be nonsense).
+ No size checking will be conducted, therefore no exceptions
+ for wrong usage (result will be nonsense).
:Example:
- >>> v = 3*vector([1,2,3,4,5])
+ >>> v = 3 * vector([1, 2, 3, 4, 5])
>>> print(v)
[3, 6, 9, 12, 15]
- >>> v = 3.*vector([1,2,3,4,5])
+ >>> v = 3. * vector([1, 2, 3, 4, 5])
>>> print(v)
[3.0, 6.0, 9.0, 12.0, 15.0]
.. seealso::
- :meth:`__mul__`
- :meth:`matrix.__mul__` for matrix * vector
+ :meth:`__mul__` and :meth:`matrix.__mul__` for matrix * vector
"""
try: # 2d list * vector (matrix * vector see matrix.__mul__)
- return vector([sum(c*d for c, d in zip(a_row, self)) for a_row in other])
+ return vector([sum(c*d for c, d in zip(a_row, self)) for
+ a_row in other])
except: # scalar * vector
return self*other
@@ -223,7 +232,7 @@ class vector(list):
r"""Outer product a @ b (new object)
.. math::
- \vec{a} \otimes \vec{b}
+ \mathbf{c} = \mathbf{a} \otimes \mathbf{b}
=
\begin{pmatrix}
a_{1}\\
@@ -246,7 +255,7 @@ class vector(list):
:Example:
- >>> m = vector([1,2,3]) @ vector([1,2,4])
+ >>> m = vector([1, 2, 3]) @ vector([1, 2, 4])
>>> print(m)
[[1, 2, 4], [2, 4, 8], [3, 6, 12]]
"""
@@ -259,17 +268,80 @@ class vector(list):
r"""Magnitude / norm of a vector
.. math::
- b = \sqrt{\sum a_i^2}
+ b = |\mathbf{a}| = \sqrt{\sum a_i^2} =
+ \sqrt{\mathbf{a} \cdot \mathbf{a}}
:Example:
- >>> norm([3, 4])
- 5
- >>> norm(vector([3, 4]))
- 5
+ >>> v = vector([3, 4])
+ >>> abs(v)
+ 5.0
"""
return math.sqrt(self * self)
+ def __lt__(self, other):
+ """Test if this object is lower (smaller) than the other object.
+
+ .. math::
+ |\mathbf{a}| \lt |\mathbf{b}|
+
+ :Example:
+
+ >>> vector([3, 2, 1]) < vector([1, 2, 3])
+ False
+ >>> vector([3, 2, 1]) < vector([1, 2, 4])
+ True
+ """
+ return abs(self) < abs(other)
+
+ def __le__(self, other):
+ """Test if this object is lower (smaller) than or equal the
+ other object.
+
+ .. math::
+ |\mathbf{a}| \le |\mathbf{b}|
+
+ :Example:
+
+ >>> vector([3, 2, 1]) <= vector([1, 2, 3])
+ True
+ >>> vector([3, 2, 1]) <= vector([1, 2, 2])
+ False
+ """
+ return abs(self) <= abs(other)
+
+ def __gt__(self, other):
+ """Test if this object is greater (larger) than the other
+ object.
+
+ .. math::
+ |\mathbf{a}| \gt |\mathbf{b}|
+
+ :Example:
+
+ >>> vector([1, 2, 3]) > vector([3, 2, 1])
+ False
+ >>> vector([1, 2, 3]) > vector([2, 2, 1])
+ True
+ """
+ return abs(self) > abs(other)
+
+ def __ge__(self, other):
+ """Test if this object is greater (larger) than or equal the
+ other object.
+
+ .. math::
+ |\mathbf{a}| \ge |\mathbf{b}|
+
+ :Example:
+
+ >>> vector([1, 2, 3]) >= vector([3, 2, 1])
+ True
+ >>> vector([1, 2, 3]) >= vector([4, 2, 1])
+ False
+ """
+ return abs(self) >= abs(other)
+
def __str__(self):
return str([*self])
@@ -328,8 +400,8 @@ class vector(list):
@staticmethod
def random(shape, lmin=0.0, lmax=1.0):
- """Returns a random vector of length n or matrix of size m rows, n
- columns filled with random numbers.
+ """Returns a random vector of length n or matrix of size m rows,
+ n columns filled with random numbers.
:Example:
@@ -351,10 +423,10 @@ class vector(list):
:type a: vector
.. math::
- \vec{e}_a = \frac{\vec{a}}{|\vec{a}|}
+ \mathbf{\hat{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}
.. seealso::
- :meth:`norm` for a norm (magnitude) of a vector
+ :meth:`__abs__` for a norm (magnitude) of a vector
"""
a_mag = abs(a)
return vector([i/a_mag for i in a])
@@ -415,15 +487,12 @@ class vector(list):
The direction of c can be found with the right-hand rule.
.. math::
- \vec{c} = \vec{a} \times \vec{b}
+ \mathbf{c} = \mathbf{a} \times \mathbf{b}
"""
return [a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0]]
- def xyz(self):
- return self[:3]
-
def rotate_x(self, theta):
r"""Rotation about the x dirction.
@@ -493,10 +562,10 @@ class vector(list):
uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
- centered at the origin will have their centers move. To avoid this,
- either scale the object when it's located at the origin, or
- perform a translation afterwards to move the object back to where
- it should be.
+ centered at the origin will have their centers move. To avoid
+ this, either scale the object when it's located at the origin,
+ or perform a translation afterwards to move the object back to
+ where it should be.
.. math::
\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
@@ -508,16 +577,17 @@ class vector(list):
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}
"""
- if not sy:
+ # if not sy is not suitable because 0 is also false
+ if sy is None:
sy = sx
sz = sx
self[:] = matrix.s(sx, sy, sz) * self
return self
def ch_cs(self, cs):
- r"""Transform this vector from its defined coordinate system to a
- new coordinate system, defined by the given coordinate system (u,
- v and w direction vectors).
+ r"""Transform this vector from its defined coordinate system to
+ a new coordinate system, defined by the given coordinate system
+ (u, v and w direction vectors).
.. math::
\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
@@ -542,21 +612,23 @@ class matrix(list):
:Example:
- >>> m = matrix([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], [0, 0, 0, 0]])
+ >>> m = matrix([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], \
+ [0, 0, 0, 0]])
>>> print(m[2])
[7, 8, 9, 0]
- >>> print(m[:,1:3])
+ >>> print(m[:, 1:3])
[[2, 3], [5, 6], [8, 9], [0, 0]]
- >>> print(m[0:2,1:3])
+ >>> print(m[0:2, 1:3])
[[2, 3], [5, 6]]
- >>> print(m[::2,::2])
+ >>> print(m[::2, ::2])
[[1, 3], [7, 9]]
"""
# index: slice(stop), slice(start, stop[, step])
- # for e. g. m[(1,3),:] -> index = ((1, 3), slice(None, None, None))
+ # for m[(1,3),:] -> index = ((1, 3), slice(None, None, None))
# use the list.__getslice__ method and convert result to vector
try: # 2d slicing (tuple of sclices)
- item = [row.__getitem__(index[1]) for row in super().__getitem__(index[0])]
+ item = [row.__getitem__(index[1]) for
+ row in super().__getitem__(index[0])]
except: # 1d slicing
item = super().__getitem__(index)
return matrix(item) if isinstance(item, list) else item
@@ -568,7 +640,7 @@ class matrix(list):
Rotates the coordinate system of vectors
.. math::
- R_{x}(\theta) =
+ \mathbf{R}_{x}(\theta) =
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & \cos \theta & -\sin \theta & 0 \\
@@ -591,7 +663,7 @@ class matrix(list):
Rotates the coordinate system of vectors
.. math::
- R_{y}(\theta) =
+ \mathbf{R}_{y}(\theta) =
\begin{bmatrix}
\cos \theta & 0 & \sin \theta & 0 \\
0 & 1 & 0 & 0 \\
@@ -614,7 +686,7 @@ class matrix(list):
Rotates the coordinate system of vectors
.. math::
- R_{z}(\theta) =
+ \mathbf{R}_{z}(\theta) =
\begin{bmatrix}
\cos \theta & -\sin \theta & 0 & 0 \\
\sin \theta & \cos \theta & 0 & 0 \\
@@ -625,14 +697,17 @@ class matrix(list):
:Example:
.. math::
- R_{z}(\theta) \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+ \mathbf{R}_{z}(\theta)
+ \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix}
+ &=
\begin{bmatrix}
\cos 90° & -\sin 90° & 0 & 0 \\
\sin 90° & \cos 90° & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}
- \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
+ \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} \\
+ &=
\begin{bmatrix}
0 & -1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
@@ -655,7 +730,7 @@ class matrix(list):
r"""Translation matrix
.. math::
- T =
+ \mathbf{T} =
\begin{bmatrix}
1 & 0 & 0 & t_x \\
0 & 1 & 0 & t_y \\
@@ -675,13 +750,13 @@ class matrix(list):
uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
- centered at the origin will have their centers move. To avoid this,
- either scale the object when it's located at the origin, or
- perform a translation afterwards to move the object back to where
- it should be.
+ centered at the origin will have their centers move. To avoid
+ this, either scale the object when it's located at the origin,
+ or perform a translation afterwards to move the object back to
+ where it should be.
.. math::
- S =
+ \mathbf{S} =
\begin{bmatrix}
s_x & 0 & 0 & 0 \\
0 & s_y & 0 & 0 \\
@@ -689,7 +764,8 @@ class matrix(list):
0 & 0 & 0 & 1
\end{bmatrix}
"""
- if not sy:
+ # if not sy is not suitable because 0 is also false
+ if sy is None:
sy = sx
sz = sx
T = matrix([[sx, 0, 0, 0],
@@ -700,9 +776,7 @@ class matrix(list):
def __mul__(self, other):
r"""Scalar multiplication, dot product (inner product) or
- matrix-vector multiplication.
-
- a * b (new object)
+ matrix-vector multiplication. (new object)
:type other: scalar, vector (or 1d list), matrix (or 2d list)
@@ -712,21 +786,25 @@ class matrix(list):
\mathbf{C} &= \mathbf{A} \cdot \mathbf{B}
.. note::
- No size checking will be conducted, therefore no exceptions for
- wrong usage (result will be nonsense).
+ No size checking will be conducted, therefore no exceptions
+ for wrong usage (result will be nonsense).
:Example:
- >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5
+ >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], \
+ [0, 0, 0, 1]]) * 5
>>> print(m)
[[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]
- >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5.
+ >>> m = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], \
+ [0, 0, 0, 1]]) * 5.
>>> print(m)
[[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]
- >>> v = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * vector([12, 12, 13])
+ >>> v = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * \
+ vector([12, 12, 13])
>>> print(v)
[75, 186, 297]
- >>> m = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])
+ >>> m = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * \
+ matrix([[12, 12, 13], [14, 15, 16], [17, 18, 19]])
>>> print(m)
[[91, 96, 102], [220, 231, 246], [349, 366, 390]]
@@ -734,18 +812,18 @@ class matrix(list):
:meth:`__rmul__`
"""
try: # matrix * matrix
- return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for b_col in zip(*other)] for a_row in self])
+ return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for
+ b_col in zip(*other)] for a_row in self])
except:
try: # matrix * vector
- return vector([sum(c*d for c, d in zip(a_row, other)) for a_row in self])
+ return vector([sum(c*d for c, d in zip(a_row, other)) for
+ a_row in self])
except: # matrix * scalar
return matrix([[a*other for a in a_row] for a_row in self])
def __rmul__(self, other):
r"""Scalar multiplication, dot product (inner product) or
- vector-matrix multiplication.
-
- a * b (new object)
+ vector-matrix multiplication. (new object)
:type other: scalar (or 1d list and 2d list)
@@ -755,27 +833,30 @@ class matrix(list):
\mathbf{C} &= \mathbf{A} \cdot \mathbf{B}
.. note::
- No size checking will be conducted, therefore no exceptions for
- wrong usage (result will be nonsense).
+ No size checking will be conducted, therefore no exceptions
+ for wrong usage (result will be nonsense).
:Example:
- >>> m = 5 * matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]]) * 5
+ >>> m = 5 * matrix([[1, 2, 3, 4], [5, 6, 7, 8], \
+ [9, 10, 11, 12], [0, 0, 0, 1]])
>>> print(m)
[[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [0, 0, 0, 5]]
- >>> m = 5. * matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [0, 0, 0, 1]])
+ >>> m = 5. * matrix([[1, 2, 3, 4], [5, 6, 7, 8], \
+ [9, 10, 11, 12], [0, 0, 0, 1]])
>>> print(m)
[[5.0, 10.0, 15.0, 20.0], [25.0, 30.0, 35.0, 40.0], [45.0, 50.0, 55.0, 60.0], [0.0, 0.0, 0.0, 5.0]]
.. seealso::
- :meth:`__mul__`
- :meth:`vector.__mul__` for vector * matrix
+ :meth:`__mul__` and :meth:`vector.__mul__` for vector * matrix
"""
try: # 2d list * matrix (matrix * matrix see matrix.__mul__)
- return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for b_col in zip(*self)] for a_row in other])
+ return matrix([[sum(c*d for c, d in zip(a_row, b_col)) for
+ b_col in zip(*self)] for a_row in other])
except:
try: # 1d list * matrix (vector * matrix see vector.__mul__)
- return vector([sum(c*d for c, d in zip(other, b_col)) for b_col in zip(*self)])
+ return vector([sum(c*d for c, d in zip(other, b_col)) for
+ b_col in zip(*self)])
except: # scalar * vector
return self*other
@@ -894,10 +975,10 @@ class matrix(list):
uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
- centered at the origin will have their centers move. To avoid this,
- either scale the object when it's located at the origin, or
- perform a translation afterwards to move the object back to where
- it should be.
+ centered at the origin will have their centers move. To avoid
+ this, either scale the object when it's located at the origin,
+ or perform a translation afterwards to move the object back to
+ where it should be.
.. math::
\begin{bmatrix}
@@ -919,7 +1000,8 @@ class matrix(list):
0 & 0 & 0 & h
\end{bmatrix}
"""
- if not sy:
+ # if not sy is not suitable because 0 is also false
+ if sy is None:
sy = sx
sz = sx
self[:] = matrix.s(sx, sy, sz) * self
diff --git a/tests/test_data.py b/tests/test_data.py
index 428fa0e..5437b01 100644
--- a/tests/test_data.py
+++ b/tests/test_data.py
@@ -12,8 +12,8 @@ import unittest
import os
import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
-from data import read, unique_ending, get_id, seq
+sys.path.insert(0, os.path.abspath('..'))
+from pylib.data import read, unique_ending, get_id, seq
class TestData(unittest.TestCase):
diff --git a/tests/test_fit.py b/tests/test_fit.py
index ee509f9..a2323e2 100644
--- a/tests/test_fit.py
+++ b/tests/test_fit.py
@@ -13,9 +13,9 @@ import unittest
import os
import sys
from pylab import array, argmax, subplot, plot, title, xlim, show, gradient, linspace
-sys.path.insert(0, os.path.abspath('../pylib'))
-from data import data_read
-from numerical.fit import gauss_fit
+sys.path.insert(0, os.path.abspath('..'))
+from pylib.data import read
+from pylib.numerical.fit import gauss_fit
class TestFit(unittest.TestCase):
@@ -23,7 +23,7 @@ class TestFit(unittest.TestCase):
def test_gauss(self):
"""test function"""
file_name = "test_fit.dat"
- x, y = data_read(file_name, 3, 2)
+ x, y = read(file_name, 3, 2)
subplot(2, 2, 1)
plot(x, y, '.-')
diff --git a/tests/test_geometry.py b/tests/test_geometry.py
index df9cf09..61fc966 100644
--- a/tests/test_geometry.py
+++ b/tests/test_geometry.py
@@ -13,69 +13,85 @@ import unittest
import os
import sys
import math
-sys.path.insert(0, os.path.abspath('../pylib'))
-from mathematics import vector
-from geometry import Direction, Point, CS, Wireframe, Polygon
+sys.path.insert(0, os.path.abspath('..'))
+from pylib.geometry import Direction, Point, CS, Wireframe, Line, Polygon, Circle
class TestGeometry(unittest.TestCase):
def test_Direction(self):
p = Direction()
self.assertIsInstance(
- p, list)
+ p,
+ list)
self.assertEqual(
- p, [1, 0, 0, 0])
+ p,
+ [1, 0, 0, 0])
self.assertEqual(
- Direction(2, 3, 4), [2, 3, 4, 0])
+ Direction(2, 3, 4),
+ [2, 3, 4, 0])
- self.assertIsInstance(
- p, vector)
+ def test_Direction_getitem(self):
self.assertEqual(
- p, vector([1, 0, 0, 0]))
+ Direction()[:3],
+ [1, 0, 0])
self.assertEqual(
- Direction(2, 3, 4), vector([2, 3, 4, 0]))
-
- def test_Direction_xyz(self):
- self.assertEqual(
- Direction().xyz(), [1, 0, 0])
- self.assertEqual(
- Direction(1, -1, 1).xyz(), [1, -1, 1])
+ Direction(1, -1, 1)[:3],
+ [1, -1, 1])
def test_Point(self):
p = Point()
self.assertIsInstance(
- p, list)
+ p,
+ list)
self.assertEqual(
- p, [0, 0, 0, 1])
+ p,
+ [0, 0, 0, 1])
self.assertEqual(
- Point(2, 3, 4), [2, 3, 4, 1])
+ Point(2, 3, 4),
+ [2, 3, 4, 1])
- self.assertIsInstance(
- p, vector)
+ def test_Point_getitem(self):
self.assertEqual(
- p, vector([0, 0, 0, 1]))
+ Point()[:3],
+ [0, 0, 0])
self.assertEqual(
- Point(2, 3, 4), vector([2, 3, 4, 1]))
+ Point(1, -1, 1)[:3],
+ [1, -1, 1])
- def test_Point_xyz(self):
+ def test_Point_rotate(self):
+ [self.assertAlmostEqual(i, j) for i, j in
+ zip(Point(1, 1, 1).rotate_x(math.pi/4), [1, 0, 1.414213562373095, 1])]
+
+ def test_CS(self):
self.assertEqual(
- Point().xyz(), [0, 0, 0])
- self.assertEqual(
- Point(1, -1, 1).xyz(), [1, -1, 1])
+ CS(),
+ [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
+
+ def test_CS_rotate(self):
+ [self.assertAlmostEqual(k, l) for i, j in
+ zip(CS().rotate_y(-math.pi/2),
+ [[0, 0.0, -1.0, 0.0], [0, 1, 0, 0], [1.0, 0.0, 0, 0.0], [0, 0, 0, 1]])
+ for k, l in zip(i, j)]
def test_Wireframe(self):
self.assertEqual(
- Wireframe().points(), [])
+ Wireframe().points(),
+ [])
# it is possible to assign other objects then Points but/and the
# class will not test if Points are used, this is just assumed
self.assertEqual(
- Wireframe([]).points(), [[]])
+ Wireframe([]).points(),
+ [[]])
self.assertEqual(
- Wireframe(Point()).points(), [[0, 0, 0, 1]])
+ Wireframe(Point()).points(),
+ [[0, 0, 0, 1]])
+
+ def test_Line(self):
self.assertEqual(
- Wireframe(Point()).points(), [vector([0, 0, 0, 1])])
+ Line().points(),
+ [[-1, 0, 0, 1], [1, 0, 0, 1]])
def test_Polygon(self):
p0 = Point()
@@ -87,6 +103,14 @@ class TestGeometry(unittest.TestCase):
pg.points(),
[[0, 0, 0, 1], [1, 0 , 0, 1], [1, 1, 1, 1], [0, 1, 1, 1], [0, 0, 0, 1]])
+ def test_Polygon_rotate(self):
+ pg = Polygon(Point(1, 1, 1)).rotate_x(math.pi/4)
+ [self.assertAlmostEqual(i, j) for i, j in
+ zip(pg.points()[0], [1, 0, 1.414213562373095, 1])]
+ [self.assertAlmostEqual(k, l) for i, j in
+ zip(pg.xyz(), ((1, 1), (0, 0), (1.414213562373095, 1.414213562373095)))
+ for k, l in zip(i, j)]
+
def test_Polygon_ch_cs(self):
# example object to rotate
p0 = Point()
@@ -103,5 +127,23 @@ class TestGeometry(unittest.TestCase):
pg.ch_cs(cs)
[self.assertAlmostEqual(i, j) for i, j in zip(pg.points(), test)]
+ def test_Circle(self):
+ cs = Circle(n=4).points()
+ test = [[1, 0, 0, 1], [0, 1, 0, 1], [-1, 0, 0, 1], [0, -1, 0 ,1], [1, 0, 0, 1]]
+ [self.assertAlmostEqual(i, j) for i, j in zip(cs, test)]
+
+ cs = Circle().points()
+ test = [[1.0, 0.0, 0, 1],
+ [0.8090169943749475, 0.5877852522924731, 0, 1],
+ [0.30901699437494745, 0.9510565162951535, 0, 1],
+ [-0.30901699437494734, 0.9510565162951536, 0, 1],
+ [-0.8090169943749473, 0.5877852522924732, 0, 1],
+ [-1.0, 1.2246467991473532e-16, 0, 1],
+ [-0.8090169943749476, -0.587785252292473, 0, 1],
+ [-0.30901699437494756, -0.9510565162951535, 0, 1],
+ [0.30901699437494723, -0.9510565162951536, 0, 1],
+ [0.8090169943749473, -0.5877852522924734, 0, 1]]
+ [self.assertAlmostEqual(k, l) for i, j in zip(cs, test) for k, l in zip(i, j) ]
+
if __name__ == '__main__':
unittest.main(verbosity=2)
diff --git a/tests/test_geometry2d.py b/tests/test_geometry2d.py
index 444c289..cbd3f30 100644
--- a/tests/test_geometry2d.py
+++ b/tests/test_geometry2d.py
@@ -14,10 +14,10 @@ import os
import sys
import math
from numpy import allclose
-sys.path.insert(0, os.path.abspath('../pylib'))
-from data import fold_list
-from geometry2d import translate_xy, rotate_xy, interpolate_hermite, lines, cubics
-from geometry2d_plot import plot_lines, plot_cubic_lines
+sys.path.insert(0, os.path.abspath('..'))
+from pylib.data import fold_list
+from pylib.geometry2d import translate_xy, rotate_xy, interpolate_hermite, lines, cubics
+from pylib.geometry2d_plot import plot_lines, plot_cubic_lines
class TestGeometry2d(unittest.TestCase):
diff --git a/tests/test_mathematics.py b/tests/test_mathematics.py
index 3769a3c..9a43e55 100644
--- a/tests/test_mathematics.py
+++ b/tests/test_mathematics.py
@@ -12,10 +12,10 @@ import unittest
import os
import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
+sys.path.insert(0, os.path.abspath('..'))
import math
-from mathematics import vector, matrix
+from pylib.mathematics import vector, matrix
class TestGeometry(unittest.TestCase):
diff --git a/tests/test_ode.py b/tests/test_ode.py
index 7b74257..365aa22 100644
--- a/tests/test_ode.py
+++ b/tests/test_ode.py
@@ -19,10 +19,10 @@ from matplotlib.pyplot import figure, subplots, plot, show
import os
import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
-from numerical.ode import (e1, e2, e4, i1, newmark_newtonraphson,
- newmark_newtonraphson_rdk)
-from numerical.ode_model import disk, disk_nm, disk_nmmdk
+sys.path.insert(0, os.path.abspath('..'))
+from pylib.numerical.ode import (e1, e2, e4, i1,
+ newmark_newtonraphson, newmark_newtonraphson_rdk)
+from pylib.numerical.ode_model import disk, disk_nm, disk_nmmdk
def plotx1rphi(x, t, title):
"""Plot plane rotation (x, y, phi)
diff --git a/tests/test_time_of_day.py b/tests/test_time_of_day.py
index f4bc20b..903a9d7 100644
--- a/tests/test_time_of_day.py
+++ b/tests/test_time_of_day.py
@@ -14,8 +14,8 @@ from time import mktime
import os
import sys
-sys.path.insert(0, os.path.abspath('../pylib'))
-from time_of_day import (in_seconds, seconds, seconds_norm,
+sys.path.insert(0, os.path.abspath('..'))
+from pylib.time_of_day import (in_seconds, seconds, seconds_norm,
minutes, minutes_norm, hours, hours_norm, days, days_norm,
transform)