# ➡️ Vector#

#bs.vector:help

Vectors are fundamental and incredibly powerful tools to manage motions, forces and… well… do physics!

Watch a demo

“With vectors, physics has found a magnificent language.”

—Richard Feynman

## 🔧 Functions#

You can find below all functions available in this module.

### Absolute max#

#bs.vector:abs_max

Get the number furthest to zero, regardless of sign.

Inputs:

Scores $vector.abs_max.[0,1,2] bs.in: Vector components. Outputs: Return | Score $vector.abs_max bs.out: Component with the value furthest from 0.

I want to get the max component of the vector (1000, 2000, 3000):

# Define the vector
scoreboard players set $vector.abs_max.0 bs.in 1000 scoreboard players set$vector.abs_max.1 bs.in 2000
scoreboard players set $vector.abs_max.2 bs.in 3000 # Get the max component function #bs.vector:abs_max # Display the result tellraw @a [{"text":" Max component: ","color":"dark_gray"},{"score":{"name":"$vector.abs_max","objective":"bs.out"},"color":"gold"}]


Credits: Aksiome, Leirof

### Absolute min#

#bs.vector:abs_min

Get the number closest to zero, regardless of sign.

Inputs:

Scores $vector.abs_min.[0,1,2] bs.in: Vector components. Outputs: Return | Score $vector.abs_min bs.out: Component with the value closest to 0.

I want to get the min component of the vector (1000, 2000, 3000):

# Define the vector
scoreboard players set $vector.abs_min.0 bs.in 1000 scoreboard players set$vector.abs_min.1 bs.in 2000
scoreboard players set $vector.abs_min.2 bs.in 3000 # Get the min component function #bs.vector:abs_min # Display the result tellraw @a [{"text":" Min component: ","color":"dark_gray"},{"score":{"name":"$vector.abs_min","objective":"bs.out"},"color":"gold"}]


Credits: Aksiome

### Basis rotation 3D#

#bs.vector:basis_rot_3d {scaling:<value>}

Get the equivalent of the vector passed in parameter in a base with a different rotation. Useful to convert absolute/relative positions into local positions.

Inputs:

Scores $vector.basis_rot_3d.pos.[0,1,2] bs.in: Vector coordinates $$=(X,Y,Z)$$ in the starting base. Scores $vector.basis_rot_3d.rot.[0,1] bs.in: Horizontal angle $$=\phi$$ (along $$=\hat{y}$$) and vertical angle $$=\theta$$ (along $$=\hat{\phi}$$) rotation (in degree) from the starting base.

Function macro:

• Arguments
• scaling: Scalar for the function’s input and output.
Outputs:

Scores $vector.basis_rot_3d.[0,1,2] bs.out: Vector coordinates $$=(X',Y',Z')$$ in the target base. Basis system This system uses the Minecraft coordinate system. Thus: • $$\hat{y}$$ is the vertical axis. • $$\phi=0$$ (starting point of the horizontal angle) is along the $$\hat{z}$$ axis. • $$\theta=0$$ (starting point of the vertical angle) is on the horizontal plane. A block is in ~2 ~5 ~10 from me, I want to have this position in local coordinate (^? ^? ^?): # One time # Relative coordinates (we multiply by 1000 to have more precision on the result, which will also be multiplied by 1000) scoreboard players set$vector.basis_rot_3d.pos.0 bs.in 2000
scoreboard players set $vector.basis_rot_3d.pos.1 bs.in 5000 scoreboard players set$vector.basis_rot_3d.pos.2 bs.in 10000

# Difference between my rotation (= that of the coondata grid ^X ^Y ^Z) and the rotation of the Minecraft blocks grid (~X ~Y ~Z)
function #bs.position:get_rot {scale:1000}
scoreboard players operation $vector.basis_rot_3d.rot.0 bs.in = @s bs.rot.h scoreboard players operation$vector.basis_rot_3d.rot.1 bs.in = @s bs.rot.v

# Perform the basic rotation
function #bs.vector:basis_rot_3d {scaling:1000}

# See the result
tellraw @a [{"text": "X = ", "color": "dark_gray"},{"score":{"name":"$vector.basis_rot_3d.0", "objective": "bs.out"}, "color": "gold"},{"text":", Y = ", "color": "dark_gray"},{"score":{"name":"$vector.basis_rot_3d.1", "objective": "bs.out"},"color":"gold"},{"text":", Z = ","color":"dark_gray"},{"score":{"name":"$vector.basis_rot_3d.2","objective":"bs.out"},"color":"gold"}]  I want to have a vector pointing to where I’m looking at, but in relative coordinates ~X ~Y ~Z: # Once # Retrieve a vector ^ ^ ^1 corresponding to a vector directed according to the orientation of the entity (we multiply by 1000 to have more precision on the result, which will also be multiplied by 1000) scoreboard players set$vector.basis_rot_3d.pos.0 bs.in 0
scoreboard players set $vector.basis_rot_3d.pos.1 bs.in 0 scoreboard players set$vector.basis_rot_3d.pos.2 bs.in 1000

# Get the orientation
function #bs.position:get_rot {scale:1000}
scoreboard players operation $vector.basis_rot_3d.rot.0 bs.in = @s bs.rot.h scoreboard players operation$vector.basis_rot_3d.rot.1 bs.in = @s bs.rot.v

# Reversal of the orientation since we want to have the relative orientation of the game grid compared to the orientation of the player (unlike the previous example)
scoreboard players operation $vector.basis_rot_3d.rot.0 bs.in *= -1 bs.const scoreboard players operation$vector.basis_rot_3d.rot.1 bs.in *= -1 bs.const

# Perform the basic rotation
function #bs.vector:basis_rot_3d {scaling:1000}

# See the result
tellraw @a [{"text": "X = ", "color": "dark_gray"},{"score":{"name":"$vector.basis_rot_3d.0", "objective": "bs.out"}, "color": "gold"},{"text":", Y = ", "color": "dark_gray"},{"score":{"name":"$vector.basis_rot_3d.1", "objective": "bs.out"},"color":"gold"},{"text":", Z = ","color":"dark_gray"},{"score":{"name":"$vector.basis_rot_3d.2","objective":"bs.out"},"color":"gold"}]  Credits: Aksiome, Leirof ### Cartesian to spherical# #bs.vector:cartesian_to_spherical {scaling:<value>} Convert cartesian coordinates to spherical coordinates. Inputs: Scores $vector.cartesian_to_spherical.[0,1,2] bs.in: Vector representing the cartesian coordinates $$=(X,Y,Z)$$.

Function macro:

• Arguments
• scaling: Scalar for the function’s input and output.
Outputs:

Scores $vector.cartesian_to_spherical.[0,1,2] bs.out: Vector representing the spherical coordinates $$=(H,V,R)$$. Spherical coordinates This system returns non conventional spherical coordinates. • $$H$$ (horizontal angle) is along the $$\hat{z}$$ axis. • $$V$$ (vertical angle) is on the horizontal plane. • $$R$$ is the radial distance. I want to convert the vector (1000, 2000, 3000) to spherical coordinates: # Define the vector scoreboard players set$vector.cartesian_to_spherical.0 bs.in 1000
scoreboard players set $vector.cartesian_to_spherical.1 bs.in 2000 scoreboard players set$vector.cartesian_to_spherical.2 bs.in 3000

# Perform the conversion
function #bs.vector:cartesian_to_spherical {scaling:1000}

# Display the result
tellraw @a [{"text":"Spherical coordinates: ","color":"dark_gray"},{"score":{"name":"$vector.cartesian_to_spherical.0","objective":"bs.out"},"color":"gold"},{"text":"°, ","color":"gold"},{"score":{"name":"$vector.cartesian_to_spherical.1","objective":"bs.out"},"color":"gold"},{"text":"°, ","color":"gold"},{"score":{"name":"$vector.cartesian_to_spherical.2","objective":"bs.out"},"color":"gold"}]  Credits: Aksiome ### Cross product# #bs.vector:cross_product {scaling:<value>} Compute the vector product between $$u$$ and $$v$$. Inputs: Scores $vector.cross_product.u.[0,1,2] bs.in: First vector components.

Scores $vector.cross_product.v.[0,1,2] bs.in: Second vector components. Function macro: • Arguments • scaling: Scalar for the function’s input and output. Outputs: Scores $vector.cross_product.[0,1,2] bs.out: Result of the operation $$=u \times v$$.

I want to perform $$u \times v$$ with $$u=(1,2,3)$$ and $$v=(4,5,6)$$:

# Define the vectors
scoreboard players set $vector.cross_product.u.0 bs.in 100 scoreboard players set$vector.cross_product.u.1 bs.in 200
scoreboard players set $vector.cross_product.u.2 bs.in 300 scoreboard players set$vector.cross_product.v.0 bs.in 400
scoreboard players set $vector.cross_product.v.1 bs.in 500 scoreboard players set$vector.cross_product.v.2 bs.in 600

# Perform the operation
function #bs.vector:cross_product {scaling:100}

# Display the result
tellraw @a [{"text":"Cross product: ","color":"dark_gray"},{"score":{"name":"$vector.cross_product.0","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.cross_product.1","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.cross_product.2","objective":"bs.out"},"color":"gold"}]  Credits: Aksiome, Majoras16 ### Dot product# #bs.vector:dot_product {scaling:<value>} Compute the scalar product between $$u$$ and $$v$$. Inputs: Scores $vector.dot_product.u.[0,1,2] bs.in: First vector components.

Scores $vector.dot_product.v.[0,1,2] bs.in: Second vector components. Function macro: • Arguments • scaling: Scalar for the function’s input and output. Outputs: Scores $vector.dot_product bs.out: Result of the operation $$=u · v$$.

I want to perform $$u \cdot v$$ with $$u=(1,2,3)$$ and $$v=(4,5,6)$$:

# Define the vectors
scoreboard players set $vector.dot_product.u.0 bs.in 100 scoreboard players set$vector.dot_product.u.1 bs.in 200
scoreboard players set $vector.dot_product.u.2 bs.in 300 scoreboard players set$vector.dot_product.v.0 bs.in 400
scoreboard players set $vector.dot_product.v.1 bs.in 500 scoreboard players set$vector.dot_product.v.2 bs.in 600

# Perform the operation
function #bs.vector:dot_product {scaling:100}

# Display the result
tellraw @a [{"text":"Dot product: ","color":"dark_gray"},{"score":{"name":"$vector.dot_product","objective":"bs.out"},"color":"gold"}]  Credits: Aksiome, Majoras16 ### Length# #bs.vector:length Compute the norm of the vector. Inputs: Scores $vector.length.[0,1,2] bs.in: Vector components.

Outputs:

Return | Score $vector.length bs.out: Vector length. Compute the length of a vector: scoreboard players set$vector.length.0 bs.in 1000
scoreboard players set $vector.length.1 bs.in 2000 scoreboard players set$vector.length.2 bs.in 3000

function #bs.vector:length

# Display the result
tellraw @a [{"text":" Vector length: ","color":"dark_gray"},{"score":{"name":"$vector.length","objective":"bs.out"}}]  Performance tip If you want to minimize the performance impact, we recomande you to use the length_squared function instead of this one when it’s possible. In fact, computing the length of a vector requires to perform square root operation which is not a simple task for a computer, especially in Minecraft. length_squared can often be used in the following cases: • You want to compare the length with a given one, then compute manually the square of the given value and compare it with the result of length_squared, which is faster than computing the real length. • You want to compare a vector length with another one, then you can compare the result of length_squared instead of computing the real length of both vectors. #bs.vector:length_squared {scaling:<value>} Compute the squared norm of the vector. Inputs: Scores $vector.length_squared.[0,1,2] bs.in: Vector components.

Function macro:

• Arguments
• scaling: Scalar for the function’s input and output.
Outputs:

Return | Score $vector.length_squared bs.out: Vector length squared. Compute the squared length of a vector: scoreboard players set$vector.length_squared.0 bs.in 1000
scoreboard players set $vector.length_squared.1 bs.in 2000 scoreboard players set$vector.length_squared.2 bs.in 3000

function #bs.vector:length_squared

# Display the result
tellraw @a [{"text":" Vector length squared: ","color":"dark_gray"},{"score":{"name":"$vector.length_squared","objective":"bs.out"}}]  Credits: Aksiome, Leirof ### Normalize# #bs.vector:normalize {scale:<scaling>} Normalize the vector by putting the length at the given scale while keeping proportions. Inputs: Scores $vector.normalize.[0,1,2] bs.in: Vector components.

Function macro:

• Arguments
• scale: Scalar for the function’s output.
Outputs:

Scores $vector.normalize.[0,1,2] bs.out: Normalized vector components. Performance tip A vector doesn’t always need to be normalized by its length. Often, the normalize_max_component function can be used instead. While this method doesn’t normalize the length, it simplifies some operations and enhances performance. Normalize the vector (1000, 2000, 3000) with a scale of 1000: # Define the vector scoreboard players set$vector.normalize.0 bs.in 1000
scoreboard players set $vector.normalize.1 bs.in 2000 scoreboard players set$vector.normalize.2 bs.in 3000

# Perform the normalization
function #bs.vector:normalize {scale:1000}

# Display the result
tellraw @a [{"text":"Normalized vector: ","color":"dark_gray"},{"score":{"name":"$vector.normalize.0","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.normalize.1","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.normalize.2","objective":"bs.out"},"color":"gold"}]  #bs.vector:normalize_max_component {scale:<scaling>} Normalize the vector by placing the largest component at the given scale while keeping proportions. Inputs: Scores $vector.normalize_max_component.[0,1,2] bs.in: Vector components.

Function macro:

• Arguments
• scale: Scalar for the function’s output.
Outputs:

Scores $vector.normalize_max_component.[0,1,2] bs.out: Normalized vector components. Score $vector.normalize_max_component.factor bs.out: Normalization factor.

Fast normalize the vector (1000, 2000, 3000) with a scale of 1000:

# Define the vector
scoreboard players set $vector.fast_normalize.0 bs.in 1000 scoreboard players set$vector.fast_normalize.1 bs.in 2000
scoreboard players set $vector.fast_normalize.2 bs.in 3000 # Perform the fast normalization function #bs.vector:fast_normalize {scale:1000} # Display the result tellraw @a [{"text":"Normalized vector: ","color":"dark_gray"},{"score":{"name":"$vector.fast_normalize.0","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.fast_normalize.1","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.fast_normalize.2","objective":"bs.out"},"color":"gold"}]


Credits: Aksiome, Leirof

### Spherical to cartesian#

#bs.vector:spherical_to_cartesian {scaling:<value>}

Convert spherical coordinates to cartesian coordinates.

Inputs:

Scores $vector.spherical_to_cartesian.[0,1,2] bs.in: Vector representing the spherical coordinates $$=(H,V,R)$$. Function macro: • Arguments • scaling: Scalar for the function’s input and output. Outputs: Scores $vector.spherical_to_cartesian.[0,1,2] bs.out: Vector representing the cartesian coordinates $$=(X,Y,Z)$$.

Spherical coordinates

This system uses non conventional spherical coordinates.

• $$H$$ (horizontal angle) is along the $$\hat{z}$$ axis.

• $$V$$ (vertical angle) is on the horizontal plane.

• $$R$$ is the radial distance.

I want to convert the spherical coordinates $$(45°, 30°, 1)$$ to cartesian coordinates:

# Define the spherical coordinates
scoreboard players set $vector.spherical_to_cartesian.0 bs.in 45000 scoreboard players set$vector.spherical_to_cartesian.1 bs.in 30000
scoreboard players set $vector.spherical_to_cartesian.2 bs.in 1000 # Perform the conversion function #bs.vector:spherical_to_cartesian {scaling:1000} # Display the result tellraw @a [{"text":"Cartesian coordinates: ","color":"dark_gray"},{"score":{"name":"$vector.spherical_to_cartesian.0","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.spherical_to_cartesian.1","objective":"bs.out"},"color":"gold"},{"text":", ","color":"gold"},{"score":{"name":"$vector.spherical_to_cartesian.2","objective":"bs.out"},"color":"gold"}]


Credits: Aksiome