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quat

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Ryan Oldenburg 2020-11-30 00:22:10 -06:00
parent 7a9bca4236
commit a307f89589
1 changed files with 107 additions and 97 deletions
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src/vmath.nim
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@ -806,52 +806,52 @@ proc `*`*(a: Mat4, b: Vec4): Vec4 =
result.z = a[2] * b.x + a[6] * b.y + a[10] * b.z + a[14] * b.w result.z = a[2] * b.x + a[6] * b.y + a[10] * b.z + a[14] * b.w
result.w = a[3] * b.x + a[7] * b.y + a[11] * b.z + a[15] * b.w result.w = a[3] * b.x + a[7] * b.y + a[11] * b.z + a[15] * b.w
proc right*(a: Mat4): Vec3 = proc right*(a: Mat4): Vec3 {.inline.} =
result.x = a[0] result.x = a[0]
result.y = a[1] result.y = a[1]
result.z = a[2] result.z = a[2]
proc `right=`*(a: var Mat4, b: Vec3) = proc `right=`*(a: var Mat4, b: Vec3) {.inline.} =
a[0] = b.x a[0] = b.x
a[1] = b.y a[1] = b.y
a[2] = b.z a[2] = b.z
proc up*(a: Mat4): Vec3 = proc up*(a: Mat4): Vec3 {.inline.} =
result.x = a[4] result.x = a[4]
result.y = a[5] result.y = a[5]
result.z = a[6] result.z = a[6]
proc `up=`*(a: var Mat4, b: Vec3) = proc `up=`*(a: var Mat4, b: Vec3) {.inline.} =
a[4] = b.x a[4] = b.x
a[5] = b.y a[5] = b.y
a[6] = b.z a[6] = b.z
proc forward*(a: Mat4): Vec3 = proc forward*(a: Mat4): Vec3 {.inline.} =
result.x = a[8] result.x = a[8]
result.y = a[9] result.y = a[9]
result.z = a[10] result.z = a[10]
proc `forward=`*(a: var Mat4, b: Vec3) = proc `forward=`*(a: var Mat4, b: Vec3) {.inline.} =
a[8] = b.x a[8] = b.x
a[9] = b.y a[9] = b.y
a[10] = b.z a[10] = b.z
proc pos*(a: Mat4): Vec3 = proc pos*(a: Mat4): Vec3 {.inline.} =
result.x = a[12] result.x = a[12]
result.y = a[13] result.y = a[13]
result.z = a[14] result.z = a[14]
proc `pos=`*(a: var Mat4, b: Vec3) = proc `pos=`*(a: var Mat4, b: Vec3) {.inline.} =
a[12] = b.x a[12] = b.x
a[13] = b.y a[13] = b.y
a[14] = b.z a[14] = b.z
proc rotationOnly*(a: Mat4): Mat4 = proc rotationOnly*(a: Mat4): Mat4 {.inline.} =
result = a result = a
result.pos = vec3(0, 0, 0) result.pos = vec3(0, 0, 0)
proc dist*(a, b: Mat4): float32 = proc dist*(a, b: Mat4): float32 =
var let
x = a[12] - b[12] x = a[12] - b[12]
y = a[13] - b[13] y = a[13] - b[13]
z = a[14] - b[14] z = a[14] - b[14]
@ -932,7 +932,7 @@ proc hrp*(m: Mat4): Vec3 =
result.z = roll result.z = roll
proc frustum*(left, right, bottom, top, near, far: float32): Mat4 = proc frustum*(left, right, bottom, top, near, far: float32): Mat4 =
var let
rl = (right - left) rl = (right - left)
tb = (top - bottom) tb = (top - bottom)
fn = (far - near) fn = (far - near)
@ -954,13 +954,13 @@ proc frustum*(left, right, bottom, top, near, far: float32): Mat4 =
result[15] = 0 result[15] = 0
proc perspective*(fovy, aspect, near, far: float32): Mat4 = proc perspective*(fovy, aspect, near, far: float32): Mat4 =
var let
top = near * tan(fovy * PI / 360.0) top = near * tan(fovy * PI / 360.0)
right = top * aspect right = top * aspect
frustum(-right, right, -top, top, near, far) frustum(-right, right, -top, top, near, far)
proc ortho*(left, right, bottom, top, near, far: float32): Mat4 = proc ortho*(left, right, bottom, top, near, far: float32): Mat4 =
var let
rl = (right - left) rl = (right - left)
tb = (top - bottom) tb = (top - bottom)
fn = (far - near) fn = (far - near)
@ -982,7 +982,7 @@ proc ortho*(left, right, bottom, top, near, far: float32): Mat4 =
result[15] = 1 result[15] = 1
proc lookAt*(eye, center, up: Vec3): Mat4 = proc lookAt*(eye, center, up: Vec3): Mat4 =
var let
eyex = eye[0] eyex = eye[0]
eyey = eye[1] eyey = eye[1]
eyez = eye[2] eyez = eye[2]
@ -1128,19 +1128,19 @@ type Quat* = object
z*: float32 z*: float32
w*: float32 w*: float32
proc quat*(x, y, z, w: float32): Quat = proc quat*(x, y, z, w: float32): Quat {.inline.} =
result.x = x result.x = x
result.y = y result.y = y
result.z = z result.z = z
result.w = w result.w = w
proc conjugate*(q: Quat): Quat = proc conjugate*(q: Quat): Quat {.inline.} =
result.w = +q.w result.w = +q.w
result.x = -q.x result.x = -q.x
result.y = -q.y result.y = -q.y
result.z = -q.z result.z = -q.z
proc length*(q: Quat): float32 = proc length*(q: Quat): float32 {.inline.} =
sqrt( sqrt(
q.w * q.w + q.w * q.w +
q.x * q.x + q.x * q.x +
@ -1155,23 +1155,23 @@ proc normalize*(q: Quat): Quat =
result.z = q.z / m result.z = q.z / m
result.w = q.w / m result.w = q.w / m
proc xyz*(q: Quat): Vec3 = proc xyz*(q: Quat): Vec3 {.inline.} =
result.x = q.x result.x = q.x
result.y = q.y result.y = q.y
result.z = q.z result.z = q.z
proc `xyz=`*(q: var Quat, v: Vec3) = proc `xyz=`*(q: var Quat, v: Vec3) {.inline.} =
q.x = v.x q.x = v.x
q.y = v.y q.y = v.y
q.z = v.z q.z = v.z
proc `-`*(a: var Quat): Quat = proc `-`*(a: var Quat): Quat {.inline.} =
result.x = -a.x result.x = -a.x
result.y = -a.y result.y = -a.y
result.z = -a.z result.z = -a.z
result.w = -a.w result.w = -a.w
proc `+`*(a: Quat, b: Quat): Quat = proc `+`*(a: Quat, b: Quat): Quat {.inline.} =
result.x = a.x + b.x result.x = a.x + b.x
result.y = a.y + b.y result.y = a.y + b.y
result.z = a.z + b.z result.z = a.z + b.z
@ -1195,7 +1195,7 @@ proc `*`*(a, b: Quat): Quat =
result.z = a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x result.z = a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x
result.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z result.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z
proc `*`*(q: Quat, v: float32): Quat = proc `*`*(q: Quat, v: float32): Quat {.inline.} =
## Multiply the quaternion by a float32. ## Multiply the quaternion by a float32.
result.x = q.x * v result.x = q.x * v
result.y = q.y * v result.y = q.y * v
@ -1204,7 +1204,7 @@ proc `*`*(q: Quat, v: float32): Quat =
proc `*`*(q: Quat, v: Vec3): Vec3 = proc `*`*(q: Quat, v: Vec3): Vec3 =
## Multiply the quaternion by a vector. ## Multiply the quaternion by a vector.
var let
x = v.x x = v.x
y = v.y y = v.y
z = v.z z = v.z
@ -1223,29 +1223,35 @@ proc `*`*(q: Quat, v: Vec3): Vec3 =
result.y = iy * qw + iw * -qy + iz * -qx - ix * -qz result.y = iy * qw + iw * -qy + iz * -qx - ix * -qz
result.z = iz * qw + iw * -qz + ix * -qy - iy * -qx result.z = iz * qw + iw * -qz + ix * -qy - iy * -qx
proc `[]`*(a: var Quat, i: int, b: float32) =
case i
of 0: a.x
of 1: a.y
of 2: a.z
of 3: a.w
else: raise newException(IndexDefect, "Index not in 0 .. 3")
proc `[]=`*(a: var Quat, i: int, b: float32) = proc `[]=`*(a: var Quat, i: int, b: float32) =
assert(i == 0 or i == 1 or i == 2 or i == 3) case i
if i == 0: of 0: a.x = b
a.x = b of 1: a.y = b
elif i == 1: of 2: a.z = b
a.y = b of 3: a.w = b
elif i == 2: else: raise newException(IndexDefect, "Index not in 0 .. 3")
a.z = b
elif i == 3:
a.w = b
proc mat3*(q: Quat): Mat3 = proc mat3*(q: Quat): Mat3 =
var xx = q.x * q.x let
var xy = q.x * q.y xx = q.x * q.x
var xz = q.x * q.z xy = q.x * q.y
var xw = q.x * q.w xz = q.x * q.z
xw = q.x * q.w
var yy = q.y * q.y yy = q.y * q.y
var yz = q.y * q.z yz = q.y * q.z
var yw = q.y * q.w yw = q.y * q.w
var zz = q.z * q.z zz = q.z * q.z
var zw = q.z * q.w zw = q.z * q.w
result[0] = 1 - 2 * (yy + zz) result[0] = 1 - 2 * (yy + zz)
result[1] = 0 + 2 * (xy - zw) result[1] = 0 + 2 * (xy - zw)
@ -1258,17 +1264,18 @@ proc mat3*(q: Quat): Mat3 =
result[8] = 1 - 2 * (xx + yy) result[8] = 1 - 2 * (xx + yy)
proc mat4*(q: Quat): Mat4 = proc mat4*(q: Quat): Mat4 =
var xx = q.x * q.x let
var xy = q.x * q.y xx = q.x * q.x
var xz = q.x * q.z xy = q.x * q.y
var xw = q.x * q.w xz = q.x * q.z
xw = q.x * q.w
var yy = q.y * q.y yy = q.y * q.y
var yz = q.y * q.z yz = q.y * q.z
var yw = q.y * q.w yw = q.y * q.w
var zz = q.z * q.z zz = q.z * q.z
var zw = q.z * q.w zw = q.z * q.w
result[00] = 1 - 2 * (yy + zz) result[00] = 1 - 2 * (yy + zz)
result[01] = 0 + 2 * (xy - zw) result[01] = 0 + 2 * (xy - zw)
@ -1288,11 +1295,11 @@ proc mat4*(q: Quat): Mat4 =
result[14] = 0 result[14] = 0
result[15] = 1.0 result[15] = 1.0
proc recifuncalSqrt*(x: float32): float32 = proc recifuncalSqrt*(x: float32): float32 {.inline.} =
1.0 / sqrt(x) 1.0 / sqrt(x)
proc quat*(m: Mat4): Quat = proc quat*(m: Mat4): Quat =
var let
m00 = m[0] m00 = m[0]
m01 = m[4] m01 = m[4]
m02 = m[8] m02 = m[8]
@ -1305,8 +1312,9 @@ proc quat*(m: Mat4): Quat =
m21 = m[6] m21 = m[6]
m22 = m[10] m22 = m[10]
var q: Quat var
var t: float32 q: Quat
t: float32
if m22 < 0: if m22 < 0:
if m00 > m11: if m00 > m11:
@ -1328,8 +1336,9 @@ proc quat*(m: Mat4): Quat =
q q
proc fromAxisAngle*(axis: Vec3, angle: float32): Quat = proc fromAxisAngle*(axis: Vec3, angle: float32): Quat =
var a = axis.normalize() let
var s = sin(angle / 2) a = axis.normalize()
s = sin(angle / 2)
result.x = a.x * s result.x = a.x * s
result.y = a.y * s result.y = a.y * s
result.z = a.z * s result.z = a.z * s
@ -1348,18 +1357,19 @@ proc toAxisAngle*(q: Quat, axis: var Vec3, angle: var float32) =
axis.z = q.z / sinAngle axis.z = q.z / sinAngle
proc quat*(heading, pitch, roll: float32): Quat = proc quat*(heading, pitch, roll: float32): Quat =
var t0 = cos(heading * 0.5) let
var t1 = sin(heading * 0.5) t0 = cos(heading * 0.5)
var t2 = cos(roll * 0.5) t1 = sin(heading * 0.5)
var t3 = sin(roll * 0.5) t2 = cos(roll * 0.5)
var t4 = cos(pitch * 0.5) t3 = sin(roll * 0.5)
var t5 = sin(pitch * 0.5) t4 = cos(pitch * 0.5)
t5 = sin(pitch * 0.5)
result.w = t0 * t2 * t4 + t1 * t3 * t5 result.w = t0 * t2 * t4 + t1 * t3 * t5
result.x = t0 * t3 * t4 - t1 * t2 * t5 result.x = t0 * t3 * t4 - t1 * t2 * t5
result.y = t0 * t2 * t5 + t1 * t3 * t4 result.y = t0 * t2 * t5 + t1 * t3 * t4
result.z = t1 * t2 * t4 - t0 * t3 * t5 result.z = t1 * t2 * t4 - t0 * t3 * t5
proc quat*(hpr: Vec3): Quat = proc quat*(hpr: Vec3): Quat {.inline.} =
quat(hpr.x, hpr.y, hpr.z) quat(hpr.x, hpr.y, hpr.z)
proc hrp*(q: Quat): Vec3 = proc hrp*(q: Quat): Vec3 =
@ -1380,7 +1390,7 @@ proc hrp*(q: Quat): Vec3 =
var t4 = +1.0 - 2.0 * (ysqr + q.z * q.z) var t4 = +1.0 - 2.0 * (ysqr + q.z * q.z)
result.x = arctan2(t3, t4) result.x = arctan2(t3, t4)
proc dot*(a: Quat, b: Quat): float32 = proc dot*(a: Quat, b: Quat): float32 {.inline.} =
a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w
proc nlerp*(a: Quat, b: Quat, v: float32): Quat = proc nlerp*(a: Quat, b: Quat, v: float32): Quat =
@ -1393,25 +1403,25 @@ proc nlerp*(a: Quat, b: Quat, v: float32): Quat =
proc `$`*(a: Quat): string = proc `$`*(a: Quat): string =
&"q({a.x:.8f}, {a.y:.8f}, {a.z:.8f}, {a.w:.8f})" &"q({a.x:.8f}, {a.y:.8f}, {a.z:.8f}, {a.w:.8f})"
proc rotate*(angle: float32, axis: Vec3): Mat4 = proc rotate*(angle: float32, axis: Vec3): Mat4 {.inline.} =
fromAxisAngle(axis, angle).mat4() fromAxisAngle(axis, angle).mat4()
proc rotateX*(angle: float32): Mat4 = proc rotateX*(angle: float32): Mat4 {.inline.} =
rotate(angle, vec3(1, 0, 0)) rotate(angle, vec3(1, 0, 0))
proc rotateY*(angle: float32): Mat4 = proc rotateY*(angle: float32): Mat4 {.inline.} =
rotate(angle, vec3(0, 1, 0)) rotate(angle, vec3(0, 1, 0))
proc rotateZ*(angle: float32): Mat4 = proc rotateZ*(angle: float32): Mat4 {.inline.} =
rotate(angle, vec3(0, 0, 1)) rotate(angle, vec3(0, 0, 1))
proc scaleMat*(scale: Vec3): Mat4 = proc scaleMat*(scale: Vec3): Mat4 {.inline.} =
result[0] = scale.x result[0] = scale.x
result[5] = scale.y result[5] = scale.y
result[10] = scale.z result[10] = scale.z
result[15] = 1.0 result[15] = 1.0
proc scaleMat*(scale: float32): Mat4 = proc scaleMat*(scale: float32): Mat4 {.inline.} =
scaleMat(vec3(scale, scale, scale)) scaleMat(vec3(scale, scale, scale))
type Rect* = object type Rect* = object