Vectors - William & Lorna

[eleonoradps]

Introduction

The task given to us is to implement vectors in 2 weeks for the GPR5204 module at SAE Institute Geneva. Here is a list of what we're going to do for vectors 2, 3 and 4.

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Vector 2

Addition

The method returns: (x + rhs.x, y + rhs.y)

Substraction

The method returns: (x - rhs.x, y - rhs.y)

Multiplication

The method returns: (x rhs.x, y rhs.y)

Division

The method returns: (x / rhs.x, y / rhs.y)

Dot product

The method returns: x v2.x + y v2.y

Cross product

The method returns: v1.x v2.y - v1.y v2.y

Magnitude

The method returns: sqrtf(x x + y y)

Sqr Magnitude

The method returns: x x + y y

Angle between

The method returns: acosf(Dot(v1, v2) / (v1.Magnitude() * v2.Magnitude()))

Lerp

We use std::clamp for t with a specific range of [0-1] Then the method returns: Vec2f(v1.x + (v2.x - v1.x) t, v1.y + (v2.y - v1.y) t)

Slerp

First, we multiply Acos(dot) by t to return the angle between v1 and the result: float theta = Mathf.Acos(Dot(v1, v2)) t Vec2f relativeVec = v2 – v1 Dot (v1, v2) relativeVec.Normalize()

Then the method returns: ((v1 cos(theta)) + relativeVec sin(theta)))

Normalize

The method returns: Vec2f (x / Magnitude(), y / Magnitude())

Rotation

First, we convert the angle from degree to radian with angle = (2 PI) - angle Then the method returns: Vec2f((v1.x cos(angle)) + (v1.y -sin(angle)), (v1.x sin(angle)) + (v1.y * cos(angle)))

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Vector 3

Addition

The method returns: (x + rhs.x, y + rhs.y, z + rhs.z)

Substraction

The method returns: (x - rhs.x, y - rhs.y, z - rhs.z)

Multiplication

The method returns: (x rhs.x, y rhs.y, z * rhs.z)

Division

The method returns: (x / rhs.x, y / rhs.y, z / rhs.z)

Dot product

The method returns: (x rhs.x + y rhs.y + z * rhs.z)

Cross product

The method returns: Vec3f (v1.y v2.z – v1.z v2.y, v1.z v2.x – v1.x v2.z, v1.x v2.y - v1.y v2.x)

Magnitude

The method returns: sqrtf(x x + y y + z * z)

Sqr Magnitude

The method returns: x x + y y + z * z

Angle between

The method returns: acosf(Dot(v1, v2) / (v1.Magnitude() * v2.Magnitude()))

Lerp

We use std::clamp for t with a specific range of [0-1] Then the method returns: Vec3f (v1 + t * (v2 – v1))

Slerp

First, we multiply Acos(dot) by t to return the angle between v1 and the final result: float theta = Mathf.Acos(Dot(v1, v2)) t Vec3f relativeVec = v2 – v1 Dot (v1, v2) relativeVec.Normalize()

Then the method returns: ((v1 cos(theta)) + relativeVec sin(theta)))

Normalize

The method returns: Vec3f (x / Magnitude(), y / Magnitude(), z / Magnitude())

Rotation

We cannot do the rotation for Vector3 since there isn’t anyone working on quaternions.

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Vector 4

Addition

The method returns: (x + rhs.x, y + rhs.y, z + rhs.z, w + rhs.w)

Substraction

The method returns: (x - rhs.x, y - rhs.y, z - rhs.z, w - rhs.w)

Multiplication

The method returns: (x rhs.x, y rhs.y, z rhs.z, w rhs.w)

Division

The method returns: (x / rhs.x, y / rhs.y, z / rhs.z, w / rhs.w)

Dot product

The method returns: (x rhs.x + y rhs.y + z rhs.z + w rhs.w)

Magnitude

The method returns: sqrtf(x x + y y + z z + w w)

Sqr Magnitude

The method returns: x x + y y + z z + w w

Lerp

We use std::clamp for t with a specific range of [0-1] Then the method returns: Vec4f (v1 + t * (v2 – v1))

Normalize

The method returns: Vec4f (x / Magnitude(), y / Magnitude(), z / Magnitude(), w / Magnitude())

[EliasFarhan]

Thanks for the overall list of methods. Some little details:

• Do not use clamp on lerp! This will allow extrapolation
• Use the maths::cos, maths::sin, maths::tan, maths::acos, maths::asin, maths::atan from maths/angle.h to guarantee compile-time angle type (https://github.com/SAE-Institute-Geneva/GPR5204_919/blob/main/include/maths/angle.h)
• Use std::sqrt instead of sqrtf`
• AngleBetween should returns a maths::radian (ref maths/angle.h)
• Do not use C# notation for Slerp, Mathf.Acos is not C++
• What does happen with normalize on zero-vector?
• How will you store the components of your math vector(std::array? three floats x,y,z? both?), something like this?

  union vector3 {
  struct { float x, y, z; } ;
  float v[3] ;
  } ;