Import std.math.vector
std.math.vector
2D, 3D, and 4D vectors of Floats.
Vec2, Vec3, and Vec4: points and directions, as Floats, in the space std.math works in: right-handed, Y up, and -Z forward. Each is a Struct of its components, x, y, z, and w, in that order with nothing between, so SIMD can work on it as it stands. Their Operators work component by component, and a Float scales: v * 2, 2 * v, and v / 2. The math on them is Functions, as on Floats: Dot, Cross, Length, Normalize, Lerp, and the rest, beside the scalar ones of their names. Lengths and distances are worked out in Doubles, so no Float overflows on the way.
Examples
Local a = Vec2(3, 4)
Expect(Length(a) == 5.0 && LengthSquared(a) == 25.0 && DistanceSquared(a, Vec2(0, 0)) == 25.0)
Expect(IsClose(Normalize(a), Vec2(0.6, 0.8)) && Cross(Vec2(1, 0), Vec2(0, 1)) == 1.0)
Expect(Reflect(Vec2(1, -1), Vec2(0, 1)) == Vec2(1, 1))
Expect(Project(Vec2(2, 3), Vec2(1, 0)) == Vec2(2, 0))
Expect(IsClose(Angle(Vec2(1, 0), Vec2(0, 1)), Deg(90)))
Expect(MoveTowards(Vec2(0, 0), Vec2(10, 0), 3) == Vec2(3, 0))
Expect(Floor(Vec2(1.5, -1.5)) == Vec2(1, -2) && Ceil(Vec2(1.5, -1.5)) == Vec2(2, -1))
Expect(Round(Vec2(1.4, 1.6)) == Vec2(1, 2) && Abs(Vec2(-1, 2)) == Vec2(1, 2))
Expect(Min(a, Vec2(4, 3)) == Vec2(3, 3) && Max(a, Vec2(4, 3)) == Vec2(4, 4))
Expect(Clamp(Vec2(-1, 9), Vec2(0, 0), Vec2(5, 5)) == Vec2(0, 5))
Expect(Perpendicular(Vec2(1, 0)) == Vec2(0, 1))
Expect(IsClose(Rotate(Vec2(1, 0), Deg(90)), Vec2(0, 1)))
Local v = Vec4(1, 2, 3, 4)
Expect(Dot(v, Vec4(1, 1, 1, 1)) == 10.0 && v.xy == Vec2(1, 2))
Expect(Lerp(Vec4(0, 0, 0, 0), v, 0.5) == Vec4(0.5, 1, 1.5, 2))
Expect(Distance(Vec3(0, 0, 0), Vec3(0, 3, 4)) == 5.0)std/math/vector.fb
Types
Vec2
struct
Public Struct Vec2 Implements Numeric, Hashable, Printable, DefaultableA point or direction in 2D.
Examples
Local v = Vec2(3, 4)
Expect(Length(v) == 5.0 && Distance(v, Vec2(0, 0)) == 5.0)
Expect(Perpendicular(Vec2(1, 0)) == Vec2(0, 1))
Expect(IsClose(Rotate(Vec2(1, 0), Deg(90)), Vec2(0, 1)))-
Its x component.
-
Its y component.
-
The zero vector, (0, 0).
-
The vector (1, 1), which multiplying leaves alone.
-
The zero vector, (0, 0).
-
The components as Ints, toward 0, as As converts them: one outside an Int's range panics.
-
Its components, as "(1, 2)".
-
The component at the index: x at 0, and y at 1. Any other index panics.
-
aplusb, component by component. -
aminusb, component by component. -
atimesb, component by component. -
adivided byb, component by component. -
atimesscale. -
scaletimesa. -
adivided byscale. -
anegated.
Vec3
struct
Public Struct Vec3 Implements Numeric, Hashable, Printable, DefaultableA point or direction in 3D.
Examples
Local right = Vec3(1, 0, 0)
Local up = Vec3(0, 1, 0)
Expect(Dot(right, up) == 0.0)
Expect(Cross(right, up) == Vec3(0, 0, 1))
Expect(Length(Vec3(3, 4, 0)) == 5.0)
Expect(Normalize(Vec3(0, 0, 9)) == Vec3(0, 0, 1))
Expect(Lerp(right, up, 0.5) == Vec3(0.5, 0.5, 0))
Expect(right * 2 + up == Vec3(2, 1, 0))-
Its x component.
-
Its y component.
-
Its z component.
-
The zero vector, (0, 0, 0).
-
The vector (1, 1, 1), which multiplying leaves alone.
-
The zero vector, (0, 0, 0).
-
Up: +Y.
-
Down: -Y.
-
Right: +X.
-
Left: -X.
-
-Z, where a camera with no rotation looks.
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Back: +Z, toward the camera.
-
Its x and y, as a Vec2.
-
The components as Ints, toward 0, as As converts them: one outside an Int's range panics.
-
Its components, as "(1, 2, 3)".
-
The component at the index: x at 0, y at 1, and z at 2. Any other index panics.
-
aplusb, component by component. -
aminusb, component by component. -
atimesb, component by component. -
adivided byb, component by component. -
atimesscale. -
scaletimesa. -
adivided byscale. -
anegated.
Vec4
struct
Public Struct Vec4 Implements Numeric, Hashable, Printable, DefaultableA point or direction in 4D, or a 3D one with a w, as a Mat4 transforms it.
-
Its x component.
-
Its y component.
-
Its z component.
-
Its w component.
-
The zero vector, (0, 0, 0, 0).
-
The vector (1, 1, 1, 1), which multiplying leaves alone.
-
The zero vector, (0, 0, 0, 0).
-
Its x and y, as a Vec2.
-
Its x, y, and z, as a Vec3.
-
Its components, as "(1, 2, 3, 4)".
-
The component at the index: x at 0, y at 1, z at 2, and w at 3. Any other index panics.
-
aplusb, component by component. -
aminusb, component by component. -
atimesb, component by component. -
adivided byb, component by component. -
atimesscale. -
scaletimesa. -
adivided byscale. -
anegated.
Functions
Dot
function
Public Function Dot(a: Vec2, b: Vec2): FloatThe sum of the products of the components: for unit vectors, the cosine of the angle between.
Dot
function
Public Function Dot(a: Vec3, b: Vec3): FloatThe sum of the products of the components: for unit vectors, the cosine of the angle between.
Dot
function
Public Function Dot(a: Vec4, b: Vec4): FloatThe sum of the products of the components.
Cross
function
Public Function Cross(a: Vec2, b: Vec2): FloatThe Z of the two as 3D vectors' Cross: above 0 when b turns counterclockwise from a.
Cross
function
Public Function Cross(a: Vec3, b: Vec3): Vec3The vector at right angles to both, by the right-hand rule: Cross(Right, Up) is Back, and its length is the area of the parallelogram the two make.
Length
function
Public Function Length(v: Vec2): FloatHow long the vector is.
Length
function
Public Function Length(v: Vec3): FloatHow long v is.
Length
function
Public Function Length(v: Vec4): FloatHow long v is.
LengthSquared
function
Public Function LengthSquared(v: Vec2): FloatThe length times itself, which takes no square root, for comparing lengths, in Floats.
LengthSquared
function
Public Function LengthSquared(v: Vec3): FloatHow long v is, times itself, which takes no square root.
LengthSquared
function
Public Function LengthSquared(v: Vec4): FloatHow long v is, times itself, which takes no square root.
Distance
function
Public Function Distance(a: Vec2, b: Vec2): FloatHow far apart the two points are.
Distance
function
Public Function Distance(a: Vec3, b: Vec3): FloatHow far apart the two points are.
DistanceSquared
function
Public Function DistanceSquared(a: Vec2, b: Vec2): FloatThe distance times itself, which takes no square root, for comparing distances, in Floats.
DistanceSquared
function
Public Function DistanceSquared(a: Vec3, b: Vec3): FloatHow far apart a and b are, times itself, which takes no square root.
Normalize
function
Public Function Normalize(v: Vec2): Vec2The vector in the same direction, of length 1, and the zero vector for the zero vector.
Normalize
function
Public Function Normalize(v: Vec3): Vec3The vector in the same direction, of length 1, and the zero vector for the zero vector.
Normalize
function
Public Function Normalize(v: Vec4): Vec4The vector in the same direction, of length 1, and the zero vector for the zero vector.
Lerp
function
Public Function Lerp(a: Vec2, b: Vec2, t: Float): Vec2The point t of the way from a to b: a at 0, and b itself at 1, though b - a
rounds.
Lerp
function
Public Function Lerp(a: Vec3, b: Vec3, t: Float): Vec3The point t of the way from a to b: a at 0, and b itself at 1, though b - a
rounds.
Lerp
function
Public Function Lerp(a: Vec4, b: Vec4, t: Float): Vec4The point t of the way from a to b: a at 0, and b itself at 1, though b - a
rounds.
Min
function
Public Function Min(a: Vec2, b: Vec2): Vec2The smaller of each component.
Min
function
Public Function Min(a: Vec3, b: Vec3): Vec3The smaller of each component.
Min
function
Public Function Min(a: Vec4, b: Vec4): Vec4The smaller of each component.
Max
function
Public Function Max(a: Vec2, b: Vec2): Vec2The larger of each component.
Max
function
Public Function Max(a: Vec3, b: Vec3): Vec3The larger of each component.
Max
function
Public Function Max(a: Vec4, b: Vec4): Vec4The larger of each component.
Clamp
function
@PanicsAtCaller Public Function Clamp(v: Vec2, low: Vec2, high: Vec2): Vec2Each component kept between low's and high's, as Clamp keeps a Float. A component whose low
is above its high panics.
Clamp
function
@PanicsAtCaller Public Function Clamp(v: Vec3, low: Vec3, high: Vec3): Vec3Each component kept between low's and high's, as Clamp keeps a Float. A component whose low
is above its high panics.
Clamp
function
@PanicsAtCaller Public Function Clamp(v: Vec4, low: Vec4, high: Vec4): Vec4Each component kept between low's and high's, as Clamp keeps a Float. A component whose low
is above its high panics.
Abs
function
Public Function Abs(v: Vec2): Vec2Each component of v without its sign.
Abs
function
Public Function Abs(v: Vec3): Vec3Each component of v without its sign.
Abs
function
Public Function Abs(v: Vec4): Vec4Each component of v without its sign.
Floor
function
Public Function Floor(v: Vec2): Vec2Each component of v rounded down.
Floor
function
Public Function Floor(v: Vec3): Vec3Each component of v rounded down.
Floor
function
Public Function Floor(v: Vec4): Vec4Each component of v rounded down.
Ceil
function
Public Function Ceil(v: Vec2): Vec2Each component of v rounded up.
Ceil
function
Public Function Ceil(v: Vec3): Vec3Each component of v rounded up.
Ceil
function
Public Function Ceil(v: Vec4): Vec4Each component of v rounded up.
Round
function
Public Function Round(v: Vec2): Vec2Each component of v rounded to the nearest whole number.
Round
function
Public Function Round(v: Vec3): Vec3Each component of v rounded to the nearest whole number.
Round
function
Public Function Round(v: Vec4): Vec4Each component of v rounded to the nearest whole number.
Reflect
function
Public Function Reflect(v: Vec2, normal: Vec2): Vec2The direction v bounces off a surface with this normal, of length 1, in: as a ball does off
a wall.
Reflect
function
Public Function Reflect(v: Vec3, normal: Vec3): Vec3The direction v bounces off a surface with this normal, of length 1, in: as a ball does off
a wall.
Project
function
Public Function Project(v: Vec2, onto: Vec2): Vec2The part of v along onto, the zero vector when onto is, worked out in Doubles.
Project
function
Public Function Project(v: Vec3, onto: Vec3): Vec3The part of v along onto, the zero vector when onto is, worked out in Doubles.
Angle
function
Public Function Angle(a: Vec2, b: Vec2): FloatThe angle between the two, in radians, from 0 to Pi, and 0 when either is the zero vector, worked out in Doubles.
Angle
function
Public Function Angle(a: Vec3, b: Vec3): FloatThe angle between the two, in radians, from 0 to Pi, and 0 when either is the zero vector, worked out in Doubles.
Rotate
function
Public Function Rotate(v: Vec2, angle: Float): Vec2The vector turned counterclockwise by the angle, in radians.
Perpendicular
function
Public Function Perpendicular(v: Vec2): Vec2The vector a quarter turn counterclockwise: (-y, x).
MoveTowards
function
Public Function MoveTowards(current: Vec2, target: Vec2, maxDistance: Float): Vec2Current moved toward target by maxDistance, or to target when it's no further, worked out
in Doubles.
MoveTowards
function
Public Function MoveTowards(current: Vec3, target: Vec3, maxDistance: Float): Vec3Current moved toward target by maxDistance, or to target when it's no further, worked out
in Doubles.
IsClose
function
Public Function IsClose(a: Vec2, b: Vec2): BoolWhether each component is close to b's, as IsClose tells for Floats.
IsClose
function
Public Function IsClose(a: Vec3, b: Vec3): BoolWhether each component is close to b's, as IsClose tells for Floats.
IsClose
function
Public Function IsClose(a: Vec4, b: Vec4): BoolWhether each component is close to b's, as IsClose tells for Floats.
IsClose
function
Public Function IsClose(a: Vec2, b: Vec2, tolerance: Float): BoolWhether each component is no further from b's than tolerance.
IsClose
function
Public Function IsClose(a: Vec3, b: Vec3, tolerance: Float): BoolWhether each component is no further from b's than tolerance.
IsClose
function
Public Function IsClose(a: Vec4, b: Vec4, tolerance: Float): BoolWhether each component is no further from b's than tolerance.
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