Lecture Notes on Vector Angles in Roblox

Introduction to Vectors in Roblox

• Vectors are essential three-number constructs in Roblox.
• Key uses include:
  • Assigning values to hinge constraints for smooth animations.
  • Determining FOV (Field of Vision) range for enemy NPCs.

Importance of Finding Angles Between Vectors

• Historically difficult due to complex math.
• Roblox now provides a vector3 angle method simplifying this process.
• Understanding the underlying math is beneficial.

Understanding Angles Between Vectors

2D Example

• Angle between vectors measured at the origin.
• Always finds the shortest (most acute) angle.
• Non-signed angle by default and up to 180 degrees.

3D Example

• Involves an imaginary plane where vectors sit.
• Plane is not aligned with any axis.
• Angle is the closest to the vectors by the plane.
• Axis perpendicular to the plane can be specified to determine angle sign.

Practical Implementation in Roblox

Setting Up in Roblox

• Create parts in Roblox: ref and target, both anchored.
• Use a script to find angles using vector3 methods.

Script Implementation

• Calculate direction as unit vector from ref to target.
• Example script setup:

  local dir = (target.position - ref.position).unit
  local angle = math.deg(vector3.xAxis:Angle(dir))
  

• Converts radians to degrees using math.deg.

Handling Angle Sign and Axis

• Roblox returns angles in radians (0 to 2π).
• Convert to degrees for intuitive understanding.
• Use additional parameters to specify axis and sign.

Application with Hinges and Servos

• Use a hinge constraint for animated parts.
• Demonstrate alignment and pointing using vectors.

Practical Setup

• Flatten the direction vector to eliminate unwanted components.
• Example:

  local flatDir = dir * Vector3.new(1, 0, 1)
  

• Define axis for determining angle sign, e.g., Vector3.yAxis for xz plane.

Advanced Applications

• Create complex systems like AI turrets using the same principles.
• Example turret tracks targets and responds dynamically.

Conclusion

• Working with vectors and angles is intuitive with practice.
• Experiment to understand behavior and create sophisticated systems.
• Final Note: Engage with the community for tutorials and further learning.