geom Documentation

About

geom (pronounced “jom”) is a a module for working with geometry in a pythonic way. The motivation behind it’s development was to use as a base for collision detection, but the functionality offered by the module offers much more depth.

Reference

Functions

geom.set_tolerance(epsilon)

Set the error tolerance for which to compare floating point numbers.

TypeError is raised if epsilon isn’t numeric. ValueError is raised if epsilon isn’t positive.

geom.is_numeric(N)

Determine if N is numeric.

N may be a single value or a collection.

Classes

Vector

class geom.Vector(components)

A Vector represents a mathematical vector for any dimension.

Overloaded Operations

len(v) gives the dimension of the vector v

abs(v) gives the magnitude of the vector v

~v gives the normalized version of the vector v

-v gives the a vector in the opposite direction but same magnitude as v

v[i] gives the vector component in the ith dimension.

a == b compare two vectors for equality

a + b adds two vectors together

a - b subtracts the vector b from the vector a

a * m multiplies all components of the vector a by a scalar m

a / m divides all components of the vector a by a non-zero scalar m

a * b computes the cross product of the a with b, where a and b

are numeric collections in R3.

a @ b computes the dot product of the the vector a and the vector b

For binary operations, as long as one of the arguments is a geom.Vector, the other argument may be any form of numeric collection of the same dimension.

Vector Methods

Vector.__init__(components)

Create a vector from components

components should be a collection of numeric values. Initializing a Vector with a collection of non-numeric values will raise a TypeError. ValueError is raised if Vector is initialized with no components.

Vector.mag()

Compute the magnitude of this vector. Equivalent to abs(v).

Vector.magSq()

Compute the square of the magnitude of this vector.

Vector.norm()

Return a normalized version of this vector. Equivalent to ~v.

Vector.normalize()

Normalize this vector.

Similar to v.norm() or ~v, but v.normalize() mutates v instead of returning a new vector. ValueError is raised if this vector is the zero vector.

Vector.add(other)

Return the sum of this vector and the vector other.

Equivalent to v + other. TypeError is raised if other is not a numeric collection the same length as this vector.

Vector.addOn(other)

Add other to this vector.

Similar to v.add(other) or v + other, but v.addOn(other) mutates this v. TypeError is raised if other is not a numeric collection. ValueError is raised if the vectors are not the same length.

Vector.sub(other)

Return the difference of this vector and the vector other.

Equivalent to v - other. TypeError is raised if other is not a numeric collection the same length as this vector.

Vector.takeAway(other)

Subtract the vector other from this vector.

Similar to v.sub(other) or v - other, but v.takeAway(other) mutates this vector. TypeError is raised if other is not a numeric collection the same length as this vector.

Vector.mul(m)

Return the product of this vector and the scalar m.

Equivalent to v * m. TypeError is raised if m is not a number.

Vector.mulBy(m)

Multiply this vector by the scalar m.

Similar to v * m or v.mul(m), but v.mulBy(m) mutates the vector v. TypeError is raised if m isn’t a number.

Vector.div(m)

Return the quotient of this vector the scalar m.

Equivalent to v / m. TypeError is raised if m isn’t a number.

Vector.divBy(m)

Divide this vector by the scalar m.

Similar to v / m or v.div(m), but v.divBy(m) mutates this the vector v. TypeError is raised if m isn’t a number.

Vector.dot(other)

Return the dot product of this vector and other.

Equivalent to v @ other. TypeError is raised if other is not a numeric collection. ValueError is raised if this vector and other are not of the same dimension.

Vector.cross(other)

Return the cross product of this vector and other.

Equivalent to v * other. TypeError is raised if other is not a numeric collection. ValueError is raised if this vector and other are not in R3.

Circle

class geom.Circle(center, radius)

A Circle stores basic circle info and provides relevant useful methods.

Circle.center

The center of the circle.

center is stored as a Vector. Setting center will raise TypeError if it’s not numeric, AttributeError if has no length, and ValueError if it’s not in R2.

Circle.radius

The radius of the circle.

Setting radius will raise TypeError if it’s not numeric and ValueError if it’s negative.

Circle.area

The area of the circle.

Defined as pi*r*r. Setting the area will change the radius of the circle. Setting the area will raise TypeError if it’s not numeric and ValueError if it’s less than zero.

Circle.circumference

The circumference of the circle.

Defined as 2*pi*r. Setting the circumference will change the radius of the circle; raises TypeError if it’s not numeric and ValueError if it’s less than zero.

Circle Methods

Circle.__init__(center, radius)

Create a circle with a given center and radius.

TypeError is raised if center is not a numeric collection or if radius is not a number. ValueError is raised if center is not in R2 or if radius is not a real non-negative number.

Circle.scaled_to(m, attr='radius')

Return a new circle scaled to m.

By default, m is used to scale the radius. Calling scaled_to with attr="area" cause m to scale the area instead of the radius, and calling it with attr="circumference" will cauese m to scale the circumference. scaled_to will raise TypeError if m isn’t numeric or if attr isn’t a string, and ValueError if m is less than zero or if attr isn’t 'radius', 'circumference', or 'area'.

Circle.scaled_by(m, attr='radius')

Return a copy of this circle scaled by a factor of m.

By default, m is used to scale the radius. Calling scaled_by with attr="area" cause m to scale the area instead of the radius. scaled_by will raise TypeError if m isn’t numeric or if attr isn’t a string, and ValueError if m is less than zero or if attr is neither 'radius' nor 'area'.

Circle.moved_to(position)

Return a copy of this circle moved to the given position.

TypeError is raised if position is not a numeric collection. ValueError is raised if position is not in R2.

Circle.moved_by(vector)

Return a copy of this circle moved by the given vector.

TypeError is raised if vector is not a numeric collection. ValueError is raised if position is not in R2.

Circle.intersects(other)

Return true if this circle intersects the geometric object other.

other may be a numeric collection in R2, or some form of a circle. TypeError is raised if other is neither of these things.