commit
c5bbf9d205
1 changed files with 47 additions and 26 deletions
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@ -1,4 +1,4 @@
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import math, random, strformat, strutils
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import hashes, math, random, strformat, strutils
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export math
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@ -79,6 +79,12 @@ func `-`*(a: Vec2): Vec2 =
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result.x = -a.x
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result.y = -a.y
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func hash*(a: Vec2): Hash =
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var h: Hash
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h = h !& hash(a.x)
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h = h !& hash(a.y)
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!$h
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func lengthSq*(a: Vec2): float32 =
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a.x * a.x + a.y * a.y
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@ -95,7 +101,7 @@ func dot*(a: Vec2, b: Vec2): float32 =
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a.x*b.x + a.y*b.y
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func dir*(at: Vec2, to: Vec2): Vec2 =
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result = (at - to).normalize()
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(at - to).normalize()
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func dir*(th: float32): Vec2 =
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vec2(cos(th), sin(th))
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@ -119,7 +125,7 @@ func inRect*(v: Vec2, a: Vec2, b: Vec2): bool =
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let
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min = vec2(min(a.x, b.x), min(a.y, b.y))
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max = vec2(max(a.x, b.x), max(a.y, b.y))
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return v.x > min.x and v.x < max.x and v.y > min.y and v.y < max.y
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v.x > min.x and v.x < max.x and v.y > min.y and v.y < max.y
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func `[]`*(a: Vec2, i: int): float32 =
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assert(i == 0 or i == 1)
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@ -150,7 +156,7 @@ func fixAngle*(angle: float32): float32 =
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angle -= PI*2
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while angle < -PI:
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angle += PI*2
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return angle
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angle
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func angle*(a: Vec2): float32 =
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## Angle of a Vec2.
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@ -174,7 +180,7 @@ func turnAngle*(a, b, speed: float32): float32 =
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turn = speed
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elif turn < -speed:
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turn = -speed
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return a + turn
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a + turn
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type Vec3* = object
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## 3D vector
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@ -259,6 +265,13 @@ func `-`*(a: var Vec3): Vec3 =
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result.y = -a.y
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result.z = -a.z
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func hash*(a: Vec3): Hash =
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var h: Hash
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h = h !& hash(a.x)
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h = h !& hash(a.y)
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h = h !& hash(a.z)
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!$h
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func lengthSq*(a: Vec3): float32 =
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a.x * a.x + a.y * a.y + a.z * a.z
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@ -269,7 +282,7 @@ func `length=`*(a: var Vec3, b: float32) =
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a *= b / a.length
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func normalize*(a: Vec3): Vec3 =
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return a / math.sqrt(a.x*a.x + a.y*a.y + a.z*a.z)
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a / math.sqrt(a.x*a.x + a.y*a.y + a.z*a.z)
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func cross*(a: Vec3, b: Vec3): Vec3 =
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result.x = a.y*b.z - a.z*b.y
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@ -277,13 +290,13 @@ func cross*(a: Vec3, b: Vec3): Vec3 =
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result.z = a.x*b.y - a.y*b.x
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func computeNormal*(a, b, c: Vec3): Vec3 =
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result = cross(c - b, b - a).normalize()
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cross(c - b, b - a).normalize()
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func dot*(a: Vec3, b: Vec3): float32 =
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a.x*b.x + a.y*b.y + a.z*b.z
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func dir*(at: Vec3, to: Vec3): Vec3 =
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result = (at - to).normalize()
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(at - to).normalize()
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func dist*(at: Vec3, to: Vec3): float32 =
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(at - to).length
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@ -302,7 +315,7 @@ func quantize*(v: Vec3, n: float32): Vec3 =
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func angleBetween*(a, b: Vec3): float32 =
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var dot = dot(a, b)
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dot = dot / (a.length * b.length)
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return arccos(dot)
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arccos(dot)
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func `[]`*(a: Vec3, i: int): float32 =
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assert(i == 0 or i == 1 or i == 2)
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@ -342,7 +355,7 @@ func zy*(a: Vec3): Vec2 =
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func almostEquals*(a, b: Vec3, precision = 1e-6): bool =
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let c = a - b
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return abs(c.x) < precision and abs(c.y) < precision and abs(c.z) < precision
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abs(c.x) < precision and abs(c.y) < precision and abs(c.z) < precision
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proc randVec3*(): Vec3 =
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## Generates a random unit vector based on
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@ -444,6 +457,14 @@ func zero*(a: var Vec4) =
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a.z = 0
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a.w = 0
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func hash*(a: Vec4): Hash =
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var h: Hash
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h = h !& hash(a.x)
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h = h !& hash(a.y)
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h = h !& hash(a.z)
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h = h !& hash(a.w)
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!$h
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func xyz*(a: Vec4): Vec3 =
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vec3(a.x, a.y, a.z)
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@ -473,7 +494,7 @@ func mat3*(a, b, c, d, e, f, g, h, i: float32): Mat3 =
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result[8] = i
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func mat3*(a: Mat3): Mat3 =
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result = a
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a
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func identity*(a: var Mat3) =
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a[0] = 1
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@ -613,7 +634,7 @@ func mat4*(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13,
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result[15] = v15
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func mat4*(a: Mat4): Mat4 =
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result = a
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a
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func identity*(): Mat4 =
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result[0] = 1
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@ -634,7 +655,7 @@ func identity*(): Mat4 =
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result[15] = 1
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func mat4*(): Mat4 =
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return identity()
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identity()
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func transpose*(a: Mat4): Mat4 =
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result[0] = a[0]
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@ -676,7 +697,7 @@ func determinant*(a: Mat4): float32 =
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a32 = a[14]
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a33 = a[15]
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return (
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(
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a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 +
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a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 +
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a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 +
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@ -846,7 +867,7 @@ func dist*(a, b: Mat4): float32 =
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x = a[12] - b[12]
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y = a[13] - b[13]
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z = a[14] - b[14]
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return sqrt(x*x + y*y + z*z)
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sqrt(x*x + y*y + z*z)
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#[
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func translate*(a: Mat4, v: Vec3): Mat4 =
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@ -902,7 +923,7 @@ func close*(a: Mat4, b: Mat4): bool =
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for i in 0..15:
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if abs(a[i] - b[i]) > 0.001:
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return false
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return true
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true
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func hrp*(m: Mat4): Vec3 =
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var heading, pitch, roll: float32
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@ -948,7 +969,7 @@ func perspective*(fovy, aspect, near, far: float32): Mat4 =
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var
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top = near * tan(fovy*PI / 360.0)
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right = top * aspect
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return frustum(-right, right, -top, top, near, far)
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frustum(-right, right, -top, top, near, far)
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func ortho*(left, right, bottom, top, near, far: float32): Mat4 =
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var
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@ -1050,7 +1071,7 @@ func lookAt*(eye, center, up: Vec3): Mat4 =
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result[15] = 1
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func toFloat32*(m: Mat4): array[16, float32] =
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return [
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[
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float32 m[00], float32 m[01], float32 m[02], float32 m[03],
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float32 m[04], float32 m[05], float32 m[06], float32 m[07],
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float32 m[08], float32 m[09], float32 m[10], float32 m[11],
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@ -1082,7 +1103,7 @@ func conjugate*(q: Quat): Quat =
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result.z = -q.z
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func length*(q: Quat): float32 =
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return sqrt(
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sqrt(
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q.w * q.w +
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q.x * q.x +
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q.y * q.y +
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@ -1229,7 +1250,7 @@ func mat4*(q: Quat): Mat4 =
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result[15] = 1.0
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func recifuncalSqrt*(x: float32): float32 =
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return 1.0/sqrt(x)
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1.0/sqrt(x)
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proc quat*(m: Mat4): Quat =
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var
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echo abs(q.length - 1.0)
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assert abs(q.length - 1.0) < 0.001
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return q
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q
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func fromAxisAngle*(axis: Vec3, angle: float32): Quat =
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var a = axis.normalize()
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@ -1335,13 +1356,13 @@ func rotate*(angle: float32, axis: Vec3): Mat4 =
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fromAxisAngle(axis, angle).mat4()
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func rotateX*(angle: float32): Mat4 =
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return rotate(angle, vec3(1, 0, 0))
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rotate(angle, vec3(1, 0, 0))
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func rotateY*(angle: float32): Mat4 =
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return rotate(angle, vec3(0, 1, 0))
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rotate(angle, vec3(0, 1, 0))
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func rotateZ*(angle: float32): Mat4 =
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return rotate(angle, vec3(0, 0, 1))
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rotate(angle, vec3(0, 0, 1))
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func scaleMat*(scale: Vec3): Mat4 =
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result[0] = scale.x
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result[15] = 1.0
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func scaleMat*(scale: float32): Mat4 =
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return scaleMat(vec3(scale, scale, scale))
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scaleMat(vec3(scale, scale, scale))
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type Rect* = object
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x*: float32
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@ -1416,4 +1437,4 @@ func overlap*(a, b: Rect): bool =
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let
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xOverlap = between(a.x, b.x, b.x + b.w) or between(b.x, a.x, a.x + a.w)
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yOverlap = between(a.y, b.y, b.y + b.h) or between(b.y, a.y, a.y + a.h)
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return xOverlap and yOverlap
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xOverlap and yOverlap
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