Before vectors: 5. Oversimplified Strings Part 1 — The Basics 🟢

<aside> ⚠️

Here, we are looking at vectors from the perspective of variables and data types, not as a mathematical concept.

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TL:DR

Fundamentals:

A vector is a value made of multiple numbers that belong together.

vector direction = {1, 0, 0};

Here, direction contains three values:

x = 1
y = 0
z = 0

Vector Operations

Vector by Vector

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A vector is applied component by component.

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// Create two vector variables
vector v1 = set(1, 2, 3);
vector v2 = set(4, 5, 6);

// Add the vectors component by component
vector vadd = v1 + v2;

// Subtract the vectors component by component
vector vsub = v1 - v2;

// Multiply the vectors component by component
vector vmul = v1 * v2;

// Divide the vectors component by component
vector vdiv = v1 / v2;

The operations are performed component by component:

v1 + v2 → {1+4, 2+5, 3+6} → {5, 7, 9}
v1 - v2 → {1-4, 2-5, 3-6} → {-3, -3, -3}
v1 * v2 → {1×4, 2×5, 3×6} → {4, 10, 18}
v1 / v2 → {1÷4, 2÷5, 3÷6} → {0.25, 0.4, 0.5}

Then your attribute output:

// Store the results as vector attributes
v@vadd = vadd;
v@vsub = vsub;
v@vmul = vmul;
v@vdiv = vdiv;

Vector by Float

<aside>

A float is applied to every component of the vector.

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// Create a vector variable
vector base = set(1, 2, 3);

// Create a float variable
float f = 2;

// Add the float to each component of the vector
vector vadd = base + f;
v@vadd = vadd;

// Multiply each component of the vector by the float
vector vmul = base * f;
v@vmul = vmul;

The float is applied to every component

base + f
{1, 2, 3} + 2
→ {1+2, 2+2, 3+2}
→ {3, 4, 5}

and

base * f
{1, 2, 3} × 2
→ {1×2, 2×2, 3×2}
→ {2, 4, 6}

Vector by Vector 2

<aside>

When operating on vectors of different sizes, VEX promotes the smaller vector to match the larger one.

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// Create a vector3 variable
vector base = set(1, 2, 3);

// Create a vector2 variable
vector2 u = set(4, 5);

// Store the vectors as attributes
v@base = base;
v@u = u;

// Add the vector2 to the vector3
// The vector2 is promoted to a vector3 by adding 0 as the third component
vector result_add = base + u;
v@result_add = result_add;

// Multiply the vector3 and vector2 component by component
// The vector2 is promoted to a vector3 by adding 0 as the third component
vector result_mult = base * u;
v@result_mult = result_mult;

base = {1, 2, 3}
u    = {4, 5}

base + u = {5, 7, 3}
base * u = {4, 10, 0}

The interesting part is the multiplication:

{1, 2, 3}
×
{4, 5, 0}
────────
{4, 10, 0}

<aside> ⚠️

The missing component becomes 0, so multiplication can actually wipe out a component.

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Continue reading:

8. Oversimplified Arrays — The Lineup 🟡