Vector2

Function reference for c-vector2 calculate

Heads up!

This is the documentation for the c-vector2 command. If you mean to read the information on c-vector3, go here.

The term vector in this document will describe a 2D vector.

2D vectors

A 2D vector is a representation of a point in two-dimensional space. You can express vectors in CalcBot with 2 or 4 components, which collectively express the magnitude and direction of the vector.

General

c-v2 c <expression>

Shorthand syntax for c-vector2 calculate.

> c-v2 c i + j
(1, 1)

c-v2 m [r | d]

Shorthand syntax for switching trigonometric modes. c-vector2 and c-vector3 both share the same trigonometric mode.

> c-v2 m r
Set vector mode to radians

> c-v2 m d
Set vector mode to degrees

Operators

All operators from c-calculate are available for use in c-vector2 calculate:

not n

Negates n. If n is a truthy value, false (0) is returned. Otherwise, true (1) is returned.

> c-v2 c not true
0

> c-v2 c not false is true
1

n!

Take the factorial of n. If n is a vector, this operation will throw an error.

> c-v2 c 6!
720

> c-v2 c (1, 2)!
Cannot take factorials of vectors.

a ^ b

Raise a to the power of b. If b is a vector, this operation will immediately throw an error. If a is a vector, but b is not an integer, this operation will also immediately throw an error. This operation will not return a complex number in any situation, unlike in c-calculate.

> c-c 2 ^ 3
8

> c-v2 c (3i + j) ^ 3
(30, 10)

> c-v2 c -4 ^ (1/2)
NaN

> c-v2 c (3i + j) ^ (1/2)
Vectors cannot be raised to decimal powers.

> c-v2 c 2 ^ j
Vectors cannot be on the right side of the '^' operator.

a * b

Multiply a and b. When operating on two vectors, this operator returns the dot product of the two vectors.

> c-v2 c 2 * 4
8

> c-v2 c (1, 2) * (5, 4, 1, 2)
-8

a / b

Divide a by b. If b is a vector, this operation will immediately throw an error.

> c-v2 c 15 / 5
3

> c-v2 c (1, 2) / 2
(0.5, 1)

> c-v2 c (1, 2) / (5, 4, 1, 2)
Vectors cannot be on the right side of the '/' operator.

a % b

Divide a by b and return the remainder of the result. This is also known as modulus division, or remainder division. If either a or b is a vector, this operation will immediately throw an error.

> c-v2 c 8 % 2
0

> c-v2 c (1, 2) % 2
Vectors cannot be used with the '%' operator.

a + b

Add a and b.

> c-v2 c 1 + 1
2

> c-v2 c (3, 4) + 2
(3, 4) + 2

> c-v2 c (3, 4) + (1, 2)
(4, 6)

a - b

Subtract b from a.

> c-v2 c 1 - 1
0

> c-v2 c (3, 4) - 2
(3, 4) - 2

> c-v2 c (3, 4) - (1, 2)
(2, 2)

a is b

Returns true (1) if a is equal to b.

> c-v2 c 3 is 1 + 2
1

> c-v2 c (1, 1) is (2 - 1, 1)
1

a nis b

Returns true (1) if a is not equal to b.

> c-v2 c 3 nis 1 + 2
0

> c-v2 c (3, 1) nis (2, 1)
1

a ais b

Returns true (1) if a is approximately equal to b. The difference between them must be less than 1 * 10 ^ -6. For vectors, this operator will compare the x and y components separately.

This operator is intended to be used when comparing the results of certain mathematical operations that produce slightly imprecise results (like prime notation).

> c-v2 c 3.0000002 ais 3
1

> c-v2 c (3, 2) ais (2.9999999, 2)
1

a anis b

Negates the behavior of the ais operator.

> c-v2 c 3 anis 3
0

> c-v2 c (5, 2) anis (1, 0)
1

a > b

Returns true (1) if a is greater than b.

> c-v2 c 3 > 2
1

a < b

Returns true (1) if a is less than b.

> c-v2 c 3 < 2
0

a >= b

Returns true (1) if a is greater than or equal to b.

> c-v2 c 3 >= 2
1

> c-v2 c 4 >= 4
1

a <= b

Returns true (1) if a is less than or equal to b.

> c-v2 c 3 <= 2
0

> c-v2 c 4 <= 4
1

a and b

Returns true if both a and b are truthy values.

> c-v2 c 3 and 4
1

> c-v2 c 3 and 0
0

a or b

Returns true if either a or b are truthy values.

> c-v2 c 3 or 4
1

> c-v2 c 3 or 0
1

> c-v2 c 0 or 0
0

Vector literals

(a, b)

Syntax for a two-dimensional two-component vector.

> c-v2 c (1, 2)
(1, 2)

(a, b, c, d)

Syntax for a two-dimensional four-component vector. Vectors of this kind are implicitly converted to their component form when used with other operations during evaluation.

> c-v2 c (1, 2, 5, 3)
(1, 2, 5, 3)

Vector constants

These constants will always be available everywhere in all of c-vector2's children commands.

• i = (1, 0)

• j = (0, 1)

• zero = (0, 0)

Modified Calculate functions

All c-calculate functions as described here are available to use in c-vector calculate, and most of them will behave the same. Some functions have been modified for use with c-vector calculate, however:

Trigonometric functions

All trigonometric functions will not operate with vector arguments.

sqrt(n)

This function will not return a complex number in any situation, unlike in c-calculate.

> c-v2 c sqrt(4)
2

> c-v2 c sqrt(-4)
NaN

abs(n)

This function will behave as expected. If n is a vector, this function will return the vector with the absolute value of each of its components (equivalent to (abs(x(n)), abs(y(n)))).

> c-v2 c abs(-4)
4

> c-v2 c abs((-2, -pi))
(2, 3.141592653589793)

pow(n, p)

If p is a vector, this function will immediately throw an error. If n is a vector, but p is not an integer, this function will also immediately throw an error. Otherwise, this function behaves as expected, except that it will not return a complex number in any situation, unlike in c-calculate. This function is implicitly called when using the alternative syntax: n ^ p.

> c-v2 c pow(2, 4)
16

> c-v2 c pow(3i + j, 3)
(30, 10)

> c-v2 c pow(3i + j, 1/2)
Vectors cannot be raised to decimal powers.

> c-v2 c pow(2, j)
Vectors cannot be on the right side of the '^' operator.

Functions that return a number

Most of the functions below available in c-vector calculate are also exposed as children commands of c-vector.

x(v)

Returns the x component of vector v.

> c-v2 c x(2i + j)
2

y(v)

Returns the y component of vector v.

> c-v2 c y(2i + j)
1

comp(v)

Returns the component of vector v.

> c-v2 c comp((2, 2, 3, 3))
(1, 1)

quad(v)

Returns the quadrant that vector v's component's head lies in. If the head is on the x-axis, 5 is returned. If the head is on the y-axis, 6 is returned.

> c-v2 c quad(2i + j)
1

> c-v2 c quad(j)
6

dir(v)

Returns the direction angle of vector v, where the unit vector i (1, 0) is 0 degrees. For example, unit vector j (0, 1)'s direction angle is 90 degrees.

> c-v2 c dir(2i + j)
26.56505117707799

mag(v)

Returns the magnitude of vector v.

> c-v2 c mag(2i + j)
2.23606797749979

sqrmag(v)

Returns the squared magnitude of vector v. If you need to compare the magnitudes of two vectors, it will usually be more efficient to compare their squared magnitudes.

> c-v2 c sqrmag(2i + j)
5

angle(v1, v2)

Returns the smallest angle between vectors v1 and v2. The returned value will always be between 0 and 180 degrees.

> c-v2 c angle(2i + j, -4i + 6j)
97.12501634890181

dot(v1, v2)

Returns the dot product of vectors v1 and v2.

> c-v2 c dot(2i + j, -4i + 6j)
-2

dist(v1, v2)

Returns the distance between the heads of vectors v1 and v2.

> c-v2 c dist(2i + j, -4i + 6j)
7.810249675906654

Functions that return a vector

polar(m, a)

Returns a vector given its magnitude (m) and direction angle (a). This is equivalent to a vector defined as (m * cos(a), m * sin(a)).

> c-v2 c polar(2, 90)
(0, 2)

unit(v)

Returns the unit vector of vector v, that is, the vector with the same direction angle as v but with a magnitude of 1.

> c-v2 c unit(2i + j)
(0.8944271909999159, 0.4472135954999579)

lerp(v1, v2, t)

Returns a new vector linearly interpolated from vector v1 to v2 by a constant t. For example, lerp(2i+j, -4i+6j, 0.5) returns the midpoint between vectors 2i+j and -4i+6j.

> c-v2 c lerp(2i + j, -4i + 6j, 0.5)
(-1, 3.5)

mid(v1, v2)

Returns the midpoint between vectors v1 and v2. This will always perform more quickly than lerp(v1, v2, 0.5).

> c-v2 c mid(2i + j, -4i + 6j)
(-1, 3.5)