Vector3

Function reference for c-vector3 calculate

Heads up!

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

The term vector in this document will describe a 3D vector.

3D vectors

A 3D vector is a representation of a point in three-dimensional space. You can express vectors in CalcBot with 3 or 6 components, which collectively express the magnitude and direction of the vector.

General

c-v3 c <expression>

Shorthand syntax for c-vector3 calculate.

> c-v3 c i + j + k
(1, 1, 1)

c-v3 m [r | d]

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

> c-v3 m r
Set vector mode to radians

> c-v3 m d
Set vector mode to degrees

Operators

All operators from c-calculate and c-vector2 calculate are available for use in c-vector3 calculate:

not n

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

> c-v3 c not true
0

> c-v3 c not false is true
1

n!

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

> c-v3 c 6!
720

> c-v3 c (1, 2, 1)!
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-v3 c 2 ^ 3
8

> c-v3 c (3i + j + k) ^ 3
(33, 11, 11)

> c-v3 c -4 ^ (1/2)
NaN

> c-v3 c (3i + j + k) ^ (1/2)
Vectors cannot be raised to decimal powers.

> c-v3 c 2 ^ (2k)
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. To compute the cross productof two vectors, see cross(v1, v2).

> c-v3 c 2 * 4
8

> c-v3 c (1, 2, 2) * (5, 4, 1, 2, 1, 3)
-5

a / b

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

> c-v3 c 15 / 5
3

> c-v3 c (1, 2, 2) / 2
(0.5, 1, 1)

> c-v3 c (1, 2, 2) / (5, 4, 1, 2, 1, 3)
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-v3 c 8 % 2
0

> c-v3 c (1, 2, 2) % 2
Vectors cannot be used with the '%' operator.

a + b

Add a and b.

> c-v3 c 1 + 1
2

> c-v3 c (3, 4, 2) + 2
(3, 4, 2) + 2

> c-v3 c (3, 4, 2) + (1, 2, 3)
(4, 6, 5)

a - b

Subtract b from a.

> c-v3 c 1 - 1
0

> c-v3 c (3, 4, 2) - 2
(3, 4, 2) - 2

> c-v3 c (3, 4, 2) - (1, 2, 3)
(2, 2, -1)

a is b

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

> c-v3 c 3 is 1 + 2
1

> c-v3 c (1, 1, 0) is (2 - 1, 1, 0)
1

a nis b

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

> c-v3 c 3 nis 1 + 2
0

> c-v3 c (3, 1, 4) nis (2, 1, 0)
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-v3 c 3.0000002 ais 3
1

> c-v3 c (3, 2, 0.9999999) ais (2.9999999, 2, 1)
1

a anis b

Negates the behavior of the ais operator.

> c-v2 c 3 anis 3
0

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

a > b

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

> c-v3 c 3 > 2
1

a < b

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

> c-v3 c 3 < 2
0

a >= b

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

> c-v3 c 3 >= 2
1

> c-v3 c 4 >= 4
1

a <= b

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

> c-v3 c 3 <= 2
0

> c-v3 c 4 <= 4
1

a and b

Returns true if both a and b are truthy values.

> c-v3 c 3 and 4
1

> c-v3 c 3 and 0
0

a or b

Returns true if either a or b are truthy values.

> c-v3 c 3 or 4
1

> c-v3 c 3 or 0
1

> c-v3 c 0 or 0
0

Vector literals

(a, b, c)

Syntax for a three-dimensional three-component vector.

> c-v3 c (1, 2, 5)
(1, 2, 5)

(a, b, c, d, e, f)

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

> c-v3 c (1, 2, 5, 3, 2, 2)
(1, 2, 5, 3, 2, 2)

Vector constants

These constants will always be available everywhere in all of c-vector3's children commands.

• i = (1, 0, 0)

• j = (0, 1, 0)

• k = (0, 0, 1)

• zero = (0, 0, 0)

Modified Vector2 functions

All c-vector2 functions as described here are available to use in c-vector2 calculate, and most of them have been adapted for use with c-vector3 calculate. There are some differences, however:

Removed functions

These functions that are available in c-vector2 calculate are not available in c-vector3 calculate(and have been replaced with similar functions):

• quad(v)

• dir(v)

Unique functions

These functions are unique to c-vector3 calculate:

z(v)

Returns the z component of vector v.

> c-v3 c z(2i + j + k)
1

oct(v)

Returns the octant that vector v's component's head lies in. If the head is on the x-axis, 9 is returned. If the head is on the y-axis, 10 is returned. If the head is on the z-axis, 11 is returned.

This function serves as the replacement for c-vector2 calculate's quad(v) function.

> c-v3 c oct(2i + j + k)
1

> c-v3 c oct(k)
11

dirx(v)

Returns the direction angle vector v makes with the x-axis.

This function, along with diry(v) and dirz(v), serves as the replacement for c-vector2 calculate's dir(v) function.

> c-v3 c dirx(k)
90

diry(v)

Returns the direction angle vector v makes with the y-axis.

This function, along with dirx(v) and dirz(v), serves as the replacement for c-vector2 calculate's dir(v) function.

> c-v3 c diry(i + j + k)
54.73561031724535

dirz(v)

Returns the direction angle vector v makes with the z-axis.

This function, along with dirx(v) and diry(v), serves as the replacement for c-vector2 calculate's dir(v) function.

> c-v3 c dirz(i - j)
90

cross(v1, v2)

Returns the cross product of vectors v1 and v2.

> c-v3 c cross((3, 1, 4), (-2, 0, 5))
(5, -23, 2)