Python. High-level General-purpose Dynamic Readable Multi-paradigm Portable
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- Nancy Benson
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1 Python High-level General-purpose Dynamic Readable Multi-paradigm Portable
2 Pre-Defined Functions Python x + y x * y x - y x / y x**y abs(x) sqrt(x) exp(x) pow(x, y) log(x) sin(x) atan(x) atan2(y, x) floor(x) Matematics x + y x y x y x/y x y x x e x x y log x sin x atan x atan y x x
3 From Mathematics to Python sin 5 2 2
4 From Mathematics to Python sin /2 + sqrt(3) + sin(2)**(5/2)
5 From Mathematics to Python sin /2 + sqrt(3) + sin(2)**(5/2) cos4 2 5 atan 3
6 From Mathematics to Python sin /2 + sqrt(3) + sin(2)**(5/2) cos4 2 5 atan 3 (cos(2/sqrt(5))**4)/atan(3)
7 From Mathematics to Python sin /2 + sqrt(3) + sin(2)**(5/2) cos4 2 5 atan 3 (cos(2/sqrt(5))**4)/atan(3) 1 log 2 (3 9 log 25)
8 From Mathematics to Python sin /2 + sqrt(3) + sin(2)**(5/2) cos4 2 5 atan 3 (cos(2/sqrt(5))**4)/atan(3) 1 log 2 (3 9 log 25) sqrt(1/log(2**abs(3-9*log(25))))
9 From Python to Mathematics log(sin(2 + floor(atan(pi))/sqrt(5)))
10 From Python to Mathematics log(sin(2 + floor(atan(pi))/sqrt(5))) log sin(2 + atan π 5 )
11 From Python to Mathematics log(sin(2 + floor(atan(pi))/sqrt(5))) log sin(2 + atan π 5 ) cos(cos(cos(0.5)))**5
12 From Python to Mathematics log(sin(2 + floor(atan(pi))/sqrt(5))) log sin(2 + atan π 5 ) cos(cos(cos(0.5)))**5 cos 5 cos cos 0.5
13 From Python to Mathematics log(sin(2 + floor(atan(pi))/sqrt(5))) log sin(2 + atan π 5 ) cos(cos(cos(0.5)))**5 cos 5 cos cos 0.5 sin(cos(sin(pi/3)/3)/3)
14 From Python to Mathematics log(sin(2 + floor(atan(pi))/sqrt(5))) log sin(2 + atan π 5 ) cos(cos(cos(0.5)))**5 cos 5 cos cos 0.5 sin(cos(sin(pi/3)/3)/3) sin cos sin π 3 3 3
15 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results
16 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x
17 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x Python:
18 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x Python: def f(x): return x*x
19 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x Python: def f(x): return x*x > f(3)
20 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x Python: def f(x): return x*x > f(3) 9
21 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x Python: def f(x): return x*x > f(3) 9 > f(5)
22 From Mathematics to Python Function A mapping between arguments and results The mapping is implicit, as it is computed when the function is applied to a set of arguments and returns the result of the computation A function accepts arguments and returns results Example: f(x) = x x Python: def f(x): return x*x > f(3) 9 > f(5) 25
23 Arithmetic in Python A number can be: Integral Rational Real Complex Number
24 Arithmetic in Python A number can be: Integral Rational Real Complex Number A number can also be: Exact Inexact Inexactness is contagious: whenever an inexact number is used in an operation, the result is inexact
25 Arithmetic in Python A number can be: Integral Rational Real Complex Number A number can also be: Exact Inexact Inexactness is contagious: whenever an inexact number is used in an operation, the result is inexact All inexact numbers above a pre-defined limit are infinite and cause an error
26 Arithmetic in Python A number can be: Integral Rational Real Complex Number A number can also be: Exact Inexact Inexactness is contagious: whenever an inexact number is used in an operation, the result is inexact All inexact numbers above a pre-defined limit are infinite and cause an error Inexactness is contagious: whenever an inexact number is used in an operation, the result is inexact
27 Arithmetic in Python A number can be: Integral Rational Real Complex Number A number can also be: Exact Inexact Inexactness is contagious: whenever an inexact number is used in an operation, the result is inexact All inexact numbers above a pre-defined limit are infinite and cause an error Inexactness is contagious: whenever an inexact number is used in an operation, the result is inexact Python uses the word float for inexact numbers
28 Arithmetic in Python Exact Numbers > 10*10
29 Arithmetic in Python Exact Numbers > 10*
30 Arithmetic in Python Exact Numbers > 10* > 10*100
31 Arithmetic in Python Exact Numbers > 10* > 10*
32 Arithmetic in Python Exact Numbers > 10* > 10* > 10**1000
33 Arithmetic in Python Exact Numbers > 10* > 10* > 10**
34 Arithmetic in Python Inexact Numbers > 10.0**10
35 Arithmetic in Python Inexact Numbers > 10.0**
36 Arithmetic in Python Inexact Numbers > 10.0** > 10.0**100
37 Arithmetic in Python Inexact Numbers > 10.0** > 10.0**100 1e+100
38 Arithmetic in Python Inexact Numbers > 10.0** > 10.0**100 1e+100 > 10.0**1000
39 Arithmetic in Python Inexact Numbers > 10.0** > 10.0**100 1e+100 > 10.0**1000 OverflowError: 'Result too large'
40 Arithmetic in Python Inexact Numbers > 10.0** > 10.0**100 1e+100 > 10.0**1000 OverflowError: 'Result too large' Inexact numbers have limited size and limited precision But they are much more efficient to compute There are no solutions, only trade-offs
41 Arithmetic in Python Rounding Errors > (4/3-1)*3-1
42 Arithmetic in Python Rounding Errors > (4/3-1)* e-16
43 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10)
44 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10)
45 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1)
46 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( )
47 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( )
48 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( ) > f( )
49 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( ) > f( )
50 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( ) > f( ) > f( )
51 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( ) > f( ) > f( ) 0.0
52 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( ) > f( ) > f( ) 0.0 > f( )
53 Arithmetic in Python Rounding Errors > (4/3-1)* e-16 Dramatic Example: f(x) = x 0.1 (10 x 10) > def f(x): return x - 0.1*(10*x - 10) > f(5.1) > f( ) > f( ) > f( ) 0.0 > f( )
54 Conditional Expressions x = { x, if x < 0 x, otherwise.
55 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression An expression whose value depends on one or more conditions if α, return β, else return γ
56 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression An expression whose value depends on one or more conditions if α, return β, else return γ return β if α, else γ
57 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression An expression whose value depends on one or more conditions if α, return β, else return γ return β if α, else γ α is the condition, β is the consequent, γ is the alternative
58 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression An expression whose value depends on one or more conditions if α, return β, else return γ return β if α, else γ α is the condition, β is the consequent, γ is the alternative Logical Expression An expression whose value is either true or false α is a logical expression
59 Conditional Expressions Logical Value x = { x, if x < 0 x, otherwise. True or False In Python: True, False False, None, 0, (and others) are considered false, anything else is considered true (including True) Conditional expressions use the logical value of the condition to evaluate the correct choice
60 Conditional Expressions x = { x, if x < 0 x, otherwise. Predicate A function (or operator) that always returns true or false < is a predicate Relational Operator A predicate that compares entities <, >, =,,, and are relational operator In Python: <, >, ==, <=, >= and!=
61 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression return β if α else γ
62 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression return β if α else γ if α, return β, else return γ
63 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression return β if α else γ if α, return β, else return γ Python: def abs(x): return -x if x < 0 else x
64 Conditional Expressions x = { x, if x < 0 x, otherwise. Conditional Expression return β if α else γ if α, return β, else return γ Python: def abs(x): return -x if x < 0 else x def abs(x): if x < 0: return -x else: return x
65 Conditional Expressions Python: max(x, y) = def max(x, y): return x if x > y else y { x, if x > y y, otherwise.
66 Conditional Expressions Python: max(x, y) = def max(x, y): return x if x > y else y def max(x, y): if x > y: return x else: return y { x, if x > y y, otherwise.
67 Conditional Expressions 1 if x < 0 sgn x = 0 if x = 0 1 otherwise
68 Conditional Expressions 1 if x < 0 sgn x = 0 if x = 0 1 otherwise 1 { if x < 0 sgn x = 0 if x = 0 otherwise 1 otherwise
69 Conditional Expressions Python: 1 if x < 0 sgn x = 0 if x = 0 1 otherwise 1 { if x < 0 sgn x = 0 if x = 0 otherwise 1 otherwise
70 Conditional Expressions Python: 1 if x < 0 sgn x = 0 if x = 0 1 otherwise 1 { if x < 0 sgn x = 0 if x = 0 otherwise 1 otherwise def signum(x): return -1 if x < 0 else 0 if x == 0 else 1
71 Conditional Expressions Python: 1 if x < 0 sgn x = 0 if x = 0 1 otherwise 1 { if x < 0 sgn x = 0 if x = 0 otherwise 1 otherwise def signum(x): return -1 if x < 0 else (0 if x == 0 else 1)
72 Conditional Expressions Python: def signum(x): if x < 0: return -1 else: if x == 0: return 0 else: return 1 1 if x < 0 sgn x = 0 if x = 0 1 otherwise 1 { if x < 0 sgn x = 0 if x = 0 otherwise 1 otherwise
73 Conditional Expressions Python: def signum(x): if x < 0: return -1 elif x == 0: return 0 else: return 1 1 if x < 0 sgn x = 0 if x = 0 1 otherwise 1 { if x < 0 sgn x = 0 if x = 0 otherwise 1 otherwise
74 Local Variables c b. a
75 Local Variables c b. a Heron s formula A = s (s a) (s b) (s c) where s = a + b + c 2
76 Local Variables Heron s formula A = s (s a) (s b) (s c) where s = a + b + c 2 Local Variable s is a local variable A local variable is an additional name That abstracts concepts That simplifies expressions That avoids repeated computations
77 Local Variables Heron s formula A = s (s a) (s b) (s c) where s = a + b + c 2 def triangle_area(a, b, c): s = (a + b + c)/2 return sqrt(s*(s - a)*(s - b)*(s - c))
78 Local Variables Heron s formula A = s (s a) (s b) (s c) where s = a + b + c 2 def triangle_area(a, b, c): s = (a + b + c)/2 return sqrt(s*(s - a)*(s - b)*(s - c)) Local Variable A variable is defined the first time it is given a value The scope of the variable is the function that contains its definition
79 Global Variables pi = def area_circle(r): return pi*r*r
80 Global Variables pi = def area_circle(r): return pi*r*r Global Variable A local variable is visible only in the function where it is defined A global variable is visible in the entire program The definition of global variables is identical to the definition of local variables, but they must be defined outside any function definition In most cases, global variables should be constants
81 Modules Every time Python is restarted, it starts in a clean state All definitions made before are lost In order to save them, put them in a file (called a module) We import the module to regain the definitions Most of Python is stored in modules
82 Modules Every time Python is restarted, it starts in a clean state All definitions made before are lost In order to save them, put them in a file (called a module) We import the module to regain the definitions Most of Python is stored in modules import math
83 Modules Every time Python is restarted, it starts in a clean state All definitions made before are lost In order to save them, put them in a file (called a module) We import the module to regain the definitions Most of Python is stored in modules import math math.sqrt(2) + math.sin(math.pi)
84 Modules Every time Python is restarted, it starts in a clean state All definitions made before are lost In order to save them, put them in a file (called a module) We import the module to regain the definitions Most of Python is stored in modules import math as m m.sqrt(2) + m.sin(m.pi)
85 Modules Every time Python is restarted, it starts in a clean state All definitions made before are lost In order to save them, put them in a file (called a module) We import the module to regain the definitions Most of Python is stored in modules from math import sqrt, sin sqrt(2) + sin(math.pi)
86 Modules Every time Python is restarted, it starts in a clean state All definitions made before are lost In order to save them, put them in a file (called a module) We import the module to regain the definitions Most of Python is stored in modules from math import * sqrt(2) + sin(pi)
87 Modules import khepri khepri.box(khepri.xyz(2,1,1), khepri.xyz(3,4,5)) khepri.cone(khepri.xyz(6,0,0), 1, khepri.xyz(8,1,5)) khepri.cone_frustum(khepri.xyz(11,1,0), 2, khepri.xyz(10,0,5), 1) khepri.sphere(khepri.xyz(8,4,5), 2) khepri.cylinder(khepri.xyz(8,7,0), 1, khepri.xyz(6,8,7)) khepri.regular_pyramid(5, khepri.xyz(-2,1,0), 1, 0, khepri.xyz(2,7,7)) khepri.torus(khepri.xyz(14,6,5), 2, 1)
88 Modules import khepri as kh kh.box(kh.xyz(2,1,1), kh.xyz(3,4,5)) kh.cone(kh.xyz(6,0,0), 1, kh.xyz(8,1,5)) kh.cone_frustum(kh.xyz(11,1,0), 2, kh.xyz(10,0,5), 1) kh.sphere(kh.xyz(8,4,5), 2) kh.cylinder(kh.xyz(8,7,0), 1, kh.xyz(6,8,7)) kh.regular_pyramid(5, kh.xyz(-2,1,0), 1, 0, kh.xyz(2,7,7)) kh.torus(kh.xyz(14,6,5), 2, 1)
89 Modules from khepri import * box(xyz(2,1,1), xyz(3,4,5)) cone(xyz(6,0,0), 1, xyz(8,1,5)) cone_frustum(xyz(11,1,0), 2, xyz(10,0,5), 1) sphere(xyz(8,4,5), 2) cylinder(xyz(8,7,0), 1, xyz(6,8,7)) regular_pyramid(5, xyz(-2,1,0), 1, 0, xyz(2,7,7)) torus(xyz(14,6,5), 2, 1)
90 Cartesian Coordinates Z Y P. z x y X
91 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2
92 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(px, py, pz, qx, qy, qz): return sqrt((qx-px)**2 + (qy-py)**2 + (qz-pz)**2)
93 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(px, py, pz, qx, qy, qz): return sqrt((qx-px)**2 + (qy-py)**2 + (qz-pz)**2) The distance between P = (2, 1, 3) and Q = (5, 6, 4) is > distance(2, 1, 3, 5, 6, 4)
94 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(px, py, pz, qx, qy, qz): return sqrt((qx-px)**2 + (qy-py)**2 + (qz-pz)**2) The distance between P = (2, 1, 3) and Q = (5, 6, 4) is > distance(2, 1, 3, 5, 6, 4) It is not as clear as in mathematics
95 Cartesian Coordinates Intermediate Point The Intermediate point between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is ( p x + q x 2, p y + q y 2, p z + q z ) 2
96 Cartesian Coordinates Intermediate Point The Intermediate point between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is ( p x + q x 2, p y + q y 2, p z + q z ) 2 def intermediate_point(px, py, pz, qx, qy, qz): return...(px+qx)/2, (py+qy)/2, (pz+qz)/2...
97 Cartesian Coordinates Intermediate Point The Intermediate point between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is ( p x + q x 2, p y + q y 2, p z + q z ) 2 def intermediate_point(px, py, pz, qx, qy, qz): return...(px+qx)/2, (py+qy)/2, (pz+qz)/2... We need to handle coordinates as an entity, and not as triplets of numbers
98 Cartesian Coordinates from khepri import *
99 Cartesian Coordinates from khepri import * > xyz(1, 2, 3)
100 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3)
101 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3))
102 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3)) 1
103 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3)) 1 > cy(xyz(1, 2, 3))
104 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3)) 1 > cy(xyz(1, 2, 3)) 2
105 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3)) 1 > cy(xyz(1, 2, 3)) 2 > cz(xyz(1, 2, 3))
106 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3)) 1 > cy(xyz(1, 2, 3)) 2 > cz(xyz(1, 2, 3)) 3 cx(xyz(x, y, z)) = x cy(xyz(x, y, z)) = y cz(xyz(x, y, z)) = z
107 Cartesian Coordinates from khepri import * > xyz(1, 2, 3) xyz(1, 2, 3) > cx(xyz(1, 2, 3)) 1 > cy(xyz(1, 2, 3)) 2 > cz(xyz(1, 2, 3)) 3 cx(xyz(x, y, z)) = x cy(xyz(x, y, z)) = y cz(xyz(x, y, z)) = z Operations for Cartesian Coordinates xyz is the constructor cx, cy, and cz, are the selectors
108 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(px, py, pz, qx, qy, qz): return sqrt((qx-px)**2 + (qy-py)**2 + (qz-pz)**2) The distance between P = (2, 1, 3) and Q = (5, 6, 4) is > distance(2, 1, 3, 5, 6, 4)
109 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(p, q): return sqrt((qx?-px?)**2 + (qy?-py?)**2 + (qz?-pz?)**2) The distance between P = (2, 1, 3) and Q = (5, 6, 4) is > distance(xyz(2, 1, 3), xyz(5, 6, 4))
110 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(p, q): return sqrt((cx(q)-cx(p))**2+(cy(q)-cy(p))**2+(cz(q)-cz(p))**2) The distance between P = (2, 1, 3) and Q = (5, 6, 4) is > distance(xyz(2, 1, 3), xyz(5, 6, 4))
111 Cartesian Coordinates Distance The distance d between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is d = (q x p x ) 2 + (q y p y ) 2 + (q z p z ) 2 def distance(p, q): return sqrt((q.x-p.x)**2 + (q.y-p.y)**2 + (q.z-p.z)**2) The distance between P = (2, 1, 3) and Q = (5, 6, 4) is > distance(xyz(2, 1, 3), xyz(5, 6, 4))
112 Cartesian Coordinates Intermediate Point The Intermediate point P m between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is P m = ( p x + q x 2, p y + q y 2, p z + q z ) 2 def intermediate_point(px, py, pz, qx, qy, qz): return...(px+qx)/2, (py+qy)/2, (pz+qz)/2...
113 Cartesian Coordinates Intermediate Point The Intermediate point P m between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is P m = ( p x + q x 2, p y + q y 2, p z + q z ) 2 def intermediate_point(p, q): return xyz((cx(p)+cx(q))/2, (cy(p)+cy(q))/2, (cz(p)+cz(q))/2)
114 Cartesian Coordinates Intermediate Point The Intermediate point P m between P = (p x, p y, p z ) and Q = (q x, q y, q z ) is P m = ( p x + q x 2, p y + q y 2, p z + q z ) 2 def intermediate_point(p, q): return xyz((p.x+q.x)/2, (p.y+q.y)/2, (p.z+q.z)/2)
115 Cartesian Coordinates > xy(1, 2)
116 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0)
117 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3)
118 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3)
119 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3)
120 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3)
121 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1)
122 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0)
123 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0) > y(2)
124 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0) > y(2) xyz(0, 2, 0)
125 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0) > y(2) xyz(0, 2, 0) > z(3)
126 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0) > y(2) xyz(0, 2, 0) > z(3) xyz(0, 0, 3)
127 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0) > y(2) xyz(0, 2, 0) > z(3) xyz(0, 0, 3) def xy(x, y): return xyz(x, y, 0) def xz(x, z): return xyz(x, 0, z) def yz(y, z): return xyz(0, y, z)
128 Cartesian Coordinates > xy(1, 2) xyz(1, 2, 0) > yz(2, 3) xyz(0, 2, 3) > xz(1, 3) xyz(1, 0, 3) > x(1) xyz(1, 0, 0) > y(2) xyz(0, 2, 0) > z(3) xyz(0, 0, 3) def xy(x, y): return xyz(x, y, 0) def xz(x, z): return xyz(x, 0, z) def yz(y, z): return xyz(0, y, z) def x(x): return xyz(x, 0, 0) def y(y): return xyz(0, y, 0) def z(z): return xyz(0, 0, z)
129 Cartesian Coordinates Example: Min. number of risers for max. riser of 0.18? Y P 1 X.... P 0
130 Cartesian Coordinates Example: Min. number of risers for max. riser of 0.18? Y P 1 X.... P 0 def minimum_number_of_steps(p0, p1): return ceil((cy(p1) - cy(p0))/0.18)
131 Cartesian Coordinates Example: Min. number of risers for max. riser of 0.18? Y P 1 X.... P 0 def minimum_number_of_steps(p0, p1): return ceil((p1.y - p0.y)/0.18)
132 Cartesian Coordinates Translation Z P Y. X
133 Cartesian Coordinates Translation Z P Y z. x y X
134 Cartesian Coordinates Translation Z P P Y z. x y X
135 Cartesian Coordinates Translation Z P P Y z z z. x x y y y X
136 Cartesian Coordinates Translation Z P V Y P z z z. x x y y y X
137 Cartesian Coordinates Translation Z P V Y P z V z z. x x y y y X
138 Cartesian Coordinates Translation Z P V Y P z V z. x x z y y z y X x y
139 Cartesian Coordinates Translation Z P V Y P z V z. x x z y y z y X x y P = P + V
140 Cartesian Coordinates Translation Z P V Y P z V z. x x z y y z y X x y V = P P
141 Cartesian Coordinates Vectors A vector represents a displacement A vector does not represent a location A vector does not have an origin or a destination A vector is created by the constructor vxyz
142 Cartesian Coordinates Vectors A vector represents a displacement A vector does not represent a location A vector does not have an origin or a destination A vector is created by the constructor vxyz def vxy(dx, dy): return vxyz(dx, dy, 0) def vxz(dx, dz): return vxyz(dx, 0, dz) def vyz(dy, dz): return vxyz(0, dy, dz)
143 Cartesian Coordinates Vectors A vector represents a displacement A vector does not represent a location A vector does not have an origin or a destination A vector is created by the constructor vxyz def vx(dx): return vxyz(dx, 0, 0) def vy(dy): return vxyz(0, dy, 0) def vz(dz): return vxyz(0, 0, dz)
144 Cartesian Coordinates Vectors A vector represents a displacement A vector does not represent a location A vector does not have an origin or a destination A vector is created by the constructor vxyz xyz(x, y, z)+vxyz( x, y, z ) xyz(x + x, y + y, z + z )
145 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1)
146 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4)
147 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4)
148 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3)
149 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5)
150 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8)
151 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1)
152 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2)
153 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2)
154 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2)
155 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2)
156 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2)
157 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2) > xyz(1,2,3) + (xyz(4,5,6) - xyz(3,2,1))
158 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2) > xyz(1,2,3) + (xyz(4,5,6) - xyz(3,2,1)) xyz(2,5,8)
159 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2) > xyz(1,2,3) + (xyz(4,5,6) - xyz(3,2,1)) xyz(2,5,8) > xyz(1,2,3) + xyz(4,5,6) - xyz(3,2,1)
160 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2) > xyz(1,2,3) + (xyz(4,5,6) - xyz(3,2,1)) xyz(2,5,8) > xyz(1,2,3) + xyz(4,5,6) - xyz(3,2,1) RuntimeError: Positions cannot be added
161 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2) > xyz(1,2,3) + (xyz(4,5,6) - xyz(3,2,1)) xyz(2,5,8) > xyz(1,2,3) + xyz(4,5,6) - xyz(3,2,1) RuntimeError: Positions cannot be added > xyz(1,2,3) - xyz(3,2,1) + xyz(4,5,6)
162 Cartesian Coordinates Examples > xyz(1,2,3) + vxyz(3,2,1) xyz(4,4,4) > xyz(1,2,3) + vx(4) xyz(5,2,3) > xyz(1,2,3) + vyz(4,5) xyz(1,6,8) > xyz(1,2,3) - yz(1,1) vxyz(1,1,2) > vxy(1,2) + vxz(1,2) vxyz(2,2,2) > vxy(1,2) - vxz(1,2) vxyz(0,2,-2) > xyz(1,2,3) + (xyz(4,5,6) - xyz(3,2,1)) xyz(2,5,8) > xyz(1,2,3) + xyz(4,5,6) - xyz(3,2,1) RuntimeError: Positions cannot be added > xyz(1,2,3) - xyz(3,2,1) + xyz(4,5,6) xyz(2,5,8)
163 Polar Coordinates Y 2π n d. X
164 Polar Coordinates. ϕ ρ x y
165 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi))
166 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0)
167 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0)
168 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0) > pol(sqrt(2), pi/4)
169 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0) > pol(sqrt(2), pi/4) xyz( , 1.0, 0)
170 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0) > pol(sqrt(2), pi/4) xyz( , 1.0, 0) > pol(1, pi/2)
171 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0) > pol(sqrt(2), pi/4) xyz( , 1.0, 0) > pol(1, pi/2) xyz( e-017, 1.0, 0)
172 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0) > pol(sqrt(2), pi/4) xyz( , 1.0, 0) > pol(1, pi/2) xyz( e-017, 1.0, 0) > pol(1, pi)
173 Polar Coordinates. ϕ ρ x y def pol(rho, phi): return xy(rho*cos(phi), rho*sin(phi)) > pol(1, 0) xyz(1, 0, 0) > pol(sqrt(2), pi/4) xyz( , 1.0, 0) > pol(1, pi/2) xyz( e-017, 1.0, 0) > pol(1, pi) xyz(-1.0, e-016, 0)
174 Polar Coordinates. ϕ ρ x y def vpol(rho, phi): return vxy(rho*cos(phi), rho*sin(phi)) > vpol(1, 0) vxyz(1, 0, 0) > vpol(sqrt(2), pi/4) vxyz( , 1.0, 0) > vpol(1, pi/2) vxyz( e-017, 1.0, 0) > vpol(1, pi) vxyz(-1.0, e-016, 0)
175 Polar Coordinates ρ P P ϕ.
176 Polar Coordinates ρ P P ϕ. > xy(1, 2) + vpol(sqrt(2), pi/4)
177 Polar Coordinates ρ P P ϕ. > xy(1, 2) + vpol(sqrt(2), pi/4) xyz(2.0, 3.0, 0.0)
178 Polar Coordinates ρ P P ϕ. > xy(1, 2) + vpol(sqrt(2), pi/4) xyz(2.0, 3.0, 0.0) > xy(1, 2) + vpol(1, 0)
179 Polar Coordinates ρ P P ϕ. > xy(1, 2) + vpol(sqrt(2), pi/4) xyz(2.0, 3.0, 0.0) > xy(1, 2) + vpol(1, 0) xyz(2.0, 2.0, 0.0)
180 Polar Coordinates ρ P P ϕ. > xy(1, 2) + vpol(sqrt(2), pi/4) xyz(2.0, 3.0, 0.0) > xy(1, 2) + vpol(1, 0) xyz(2.0, 2.0, 0.0) > xy(1, 2) + vpol(1, pi/2)
181 Polar Coordinates ρ P P ϕ. > xy(1, 2) + vpol(sqrt(2), pi/4) xyz(2.0, 3.0, 0.0) > xy(1, 2) + vpol(1, 0) xyz(2.0, 2.0, 0.0) > xy(1, 2) + vpol(1, pi/2) xyz(1.0, 3.0, 0.0)
182 Geometric Modeling
183 Geometric Modeling For AutoCAD from khepri.autocad import *
184 Geometric Modeling For AutoCAD from khepri.autocad import * For Rhino from khepri.rhino import *
185 Geometric Modeling.
186 Geometric Modeling For AutoCAD from khepri.autocad import *. circle(pol(0, 0), 4) circle(pol(4, pi/4), 2) circle(pol(6, pi/4), 1)
187 Geometric Modeling For AutoCAD from khepri.autocad import *. circle(pol(0, 0), 4) circle(pol(4, pi/4), 2) circle(pol(6, pi/4), 1) For Rhino from khepri.rhino import * circle(pol(0, 0), 4) circle(pol(4, pi/4), 2) circle(pol(6, pi/4), 1)
188 Geometric Modeling polygon(pol(1, 2*pi*0/5), pol(1, 2*pi*1/5), pol(1, 2*pi*2/5), pol(1, 2*pi*3/5), pol(1, 2*pi*4/5))
189 Geometric Modeling polygon(pol(1, 2*pi*0/5), pol(1, 2*pi*1/5), pol(1, 2*pi*2/5), pol(1, 2*pi*3/5), pol(1, 2*pi*4/5)).
190 Geometric Modeling regular_polygon(5).
191 Geometric Modeling regular_polygon(3, xy(0, 0), 1, 0, True) regular_polygon(3, xy(0, 0), 1, pi/3, True) regular_polygon(4, xy(3, 0), 1, 0, True) regular_polygon(4, xy(3, 0), 1, pi/4, True) regular_polygon(5, xy(6, 0), 1, 0, True) regular_polygon(5, xy(6, 0), 1, pi/5, True)
192 Geometric Modeling regular_polygon(3, xy(0, 0), 1, 0, True) regular_polygon(3, xy(0, 0), 1, pi/3, True) regular_polygon(4, xy(3, 0), 1, 0, True) regular_polygon(4, xy(3, 0), 1, pi/4, True) regular_polygon(5, xy(6, 0), 1, 0, True) regular_polygon(5, xy(6, 0), 1, pi/5, True).
193 Geometric Modeling rectangle(xy(0, 1), xy(3, 2)) rectangle(xy(3, 2), 1, 2)
194 Geometric Modeling rectangle(xy(0, 1), xy(3, 2)) rectangle(xy(3, 2), 1, 2).
195 Side Effects rectangle(xy(0, 1), xy(3, 2)) rectangle(xy(3, 2), 1, 2).
196 Side Effects rectangle(xy(0, 1), xy(3, 2)) rectangle(xy(3, 2), 1, 2) Side Effects. Every Python expression has a value Some Python expressions also have a side effect All shape-producing expressions cause a side effect on the CAD tool Side effects can be composed by sequencing them A function that only does side effects returns nothing
197 Side Effects. P r P r
198 Side Effects. P r P r def circle_square(p, r, inscribed): if inscribed: creates a circle and a square inscribed in the circle else: creates a circle and a square circumscribed in the circle
199 Side Effects. P r P r def circle_square(p, r, inscribed): if inscribed: creates a circle creates a square inscribed in the circle else: creates a circle creates a square circumscribed in the circle
200 Side Effects. P r P r def circle_square(p, r, inscribed): if inscribed: circle(p, r) rectangle(p + vpol(r, 5/4*pi), p + vpol(r, 1/4*pi)) else: circle(p, r) rectangle(p + vxy(-r, -r), p + vxy(r, r))
201 Side Effects. P r P r def circle_square(p, r, inscribed): circle(p, r) if inscribed: rectangle(p + vpol(r, 5/4*pi), p + vpol(r, 1/4*pi)) else: rectangle(p + vxy(-r, -r), p + vxy(r, r))
LOWELL WEEKLY JOURNAL
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