MyouProject/vmath
3
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Merge pull request #22 from guzba/master

Browse source 
mat3, mat4 stuff
This commit is contained in:
treeform 2020-11-29 23:15:57 -08:00 committed by GitHub
commit 62a8b39bb1
No known key found for this signature in database
GPG key ID: 4AEE18F83AFDEB23
2 changed files with 225 additions and 240 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

449
src/vmath.nim
View file

@ -507,44 +507,32 @@ type Mat3* = array[9, float32] ## 3x3 Matrix
template `[]`*(a: Mat3, i, j: int): float32 = a[i * 3 + j] template `[]`*(a: Mat3, i, j: int): float32 = a[i * 3 + j]
template `[]=`*(a: Mat3, i, j: int, v: float32) = a[i * 3 + j] = v template `[]=`*(a: Mat3, i, j: int, v: float32) = a[i * 3 + j] = v
proc mat3*(a, b, c, d, e, f, g, h, i: float32): Mat3 = proc mat3*(a, b, c, d, e, f, g, h, i: float32): Mat3 {.inline.} =
result[0] = a [
result[1] = b a, b, c,
result[2] = c d, e, f,
result[3] = d g, h, i
result[4] = e ]
result[5] = f
result[6] = g
result[7] = h
result[8] = i
proc mat3*(a: Mat3): Mat3 = proc mat3*(a: Mat3): Mat3 {.inline.} =
a a
proc identity*(a: var Mat3) = proc identity*(a: var Mat3) {.inline.} =
a[0] = 1 a = [
a[1] = 0 1.float32, 0, 0,
a[2] = 0 0, 1, 0,
a[3] = 0 0, 0, 1
a[4] = 1 ]
a[5] = 0
a[6] = 0
a[7] = 0
a[8] = 1
proc mat3*(): Mat3 {.inline.} = proc mat3*(): Mat3 {.inline.} =
result.identity() result.identity()
proc transpose*(a: Mat3): Mat3 = proc transpose*(a: Mat3): Mat3 {.inline.} =
result[0] = a[0] [
result[1] = a[3] a[0, 0], a[1, 0], a[2, 0],
result[2] = a[6] a[0, 1], a[1, 1], a[2, 1],
result[3] = a[1] a[0, 2], a[1, 2], a[2, 2]
result[4] = a[4] ]
result[5] = a[7]
result[6] = a[2]
result[7] = a[5]
result[8] = a[8]
proc `$`*(a: Mat3): string = proc `$`*(a: Mat3): string =
&"""[{a[0]:.4f}, {a[1]:.4f}, {a[2]:.4f}, &"""[{a[0]:.4f}, {a[1]:.4f}, {a[2]:.4f},
@ -562,77 +550,67 @@ proc `*`*(a: Mat3, b: Mat3): Mat3 =
result[2, 1] += b[2, 0] * a[0, 1] + b[2, 1] * a[1, 1] + b[2, 2] * a[2, 1] result[2, 1] += b[2, 0] * a[0, 1] + b[2, 1] * a[1, 1] + b[2, 2] * a[2, 1]
result[2, 2] += b[2, 0] * a[0, 2] + b[2, 1] * a[1, 2] + b[2, 2] * a[2, 2] result[2, 2] += b[2, 0] * a[0, 2] + b[2, 1] * a[1, 2] + b[2, 2] * a[2, 2]
proc scale*(a: Mat3, v: Vec2): Mat3 = proc scale*(a: Mat3, v: Vec2): Mat3 {.inline.} =
result[0] = v.x * a[0] [
result[1] = v.x * a[1] v.x * a[0], v.x * a[1], v.x * a[2],
result[2] = v.x * a[2] v.y * a[3], v.y * a[4], v.y * a[5],
result[3] = v.y * a[3] a[6], a[7], a[8]
result[4] = v.y * a[4] ]
result[5] = v.y * a[5]
result[6] = a[6]
result[7] = a[7]
result[8] = a[8]
proc scale*(a: Mat3, v: Vec3): Mat3 = proc scale*(a: Mat3, v: Vec3): Mat3 {.inline.} =
result[0] = v.x * a[0] [
result[1] = v.x * a[1] v.x * a[0], v.x * a[1], v.x * a[2],
result[2] = v.x * a[2] v.y * a[3], v.y * a[4], v.y * a[5],
result[3] = v.y * a[3] v.z * a[6], v.z * a[7], v.z * a[8]
result[4] = v.y * a[4] ]
result[5] = v.y * a[5]
result[6] = v.z * a[6]
result[7] = v.z * a[7]
result[8] = v.z * a[8]
proc translate*(v: Vec2): Mat3 = proc translate*(v: Vec2): Mat3 {.inline.} =
result[0, 0] = 1 [
result[1, 1] = 1 1.float32, 0, 0,
result[2, 0] = v.x 0, 1, 0,
result[2, 1] = v.y v.x, v.y, 1
result[2, 2] = 1 ]
proc scale*(v: Vec2): Mat3 = proc scale*(v: Vec2): Mat3 {.inline.} =
result[0, 0] = v.x [
result[1, 1] = v.y v.x, 0, 0,
result[2, 2] = 1 0, v.y, 0,
0, 0, 1
]
proc rotationMat3*(angle: float32): Mat3 = proc rotationMat3*(angle: float32): Mat3 {.inline.} =
# Create a matrix from an angle. # Create a matrix from an angle.
let let
sin = sin(angle) sin = sin(angle)
cos = cos(angle) cos = cos(angle)
result[0, 0] = cos result = [
result[0, 1] = -sin cos, -sin, 0,
result[0, 2] = 0 sin, cos, 0,
0, 0, 1
]
result[1, 0] = sin proc rotate*(a: Mat3, angle: float32): Mat3 {.inline.} =
result[1, 1] = cos
result[1, 2] = 0
result[2, 0] = 0
result[2, 1] = 0
result[2, 2] = 1
proc rotate*(a: Mat3, angle: float32): Mat3 =
# Rotates a matrix by an angle. # Rotates a matrix by an angle.
a * rotationMat3(angle) a * rotationMat3(angle)
proc `*`*(a: Mat3, b: Vec2): Vec2 = proc `*`*(a: Mat3, b: Vec2): Vec2 =
result.x = a[0, 0]*b.x + a[1, 0]*b.y + a[2, 0] result.x = a[0, 0] * b.x + a[1, 0] * b.y + a[2, 0]
result.y = a[0, 1]*b.x + a[1, 1]*b.y + a[2, 1] result.y = a[0, 1] * b.x + a[1, 1] * b.y + a[2, 1]
proc `*`*(a: Mat3, b: Vec3): Vec3 = proc `*`*(a: Mat3, b: Vec3): Vec3 =
result.x = a[0, 0]*b.x + a[1, 0]*b.y + a[2, 0]*b.z result.x = a[0, 0] * b.x + a[1, 0] * b.y + a[2, 0] * b.z
result.y = a[0, 1]*b.x + a[1, 1]*b.y + a[2, 1]*b.z result.y = a[0, 1] * b.x + a[1, 1] * b.y + a[2, 1] * b.z
result.z = a[0, 2]*b.x + a[1, 2]*b.y + a[2, 2]*b.z result.z = a[0, 2] * b.x + a[1, 2] * b.y + a[2, 2] * b.z
proc inverse*(a: Mat3): Mat3 = proc inverse*(a: Mat3): Mat3 =
let determinant = ( let
a[0, 0] * (a[1, 1] * a[2, 2] - a[2, 1] * a[1, 2]) - determinant = (
a[0, 1] * (a[1, 0] * a[2, 2] - a[1, 2] * a[2, 0]) + a[0, 0] * (a[1, 1] * a[2, 2] - a[2, 1] * a[1, 2]) -
a[0, 2] * (a[1, 0] * a[2, 1] - a[1, 1] * a[2, 0]) a[0, 1] * (a[1, 0] * a[2, 2] - a[1, 2] * a[2, 0]) +
) a[0, 2] * (a[1, 0] * a[2, 1] - a[1, 1] * a[2, 0])
let invDet = 1 / determinant )
invDet = 1 / determinant
result[0, 0] = (a[1, 1] * a[2, 2] - a[2, 1] * a[1, 2]) * invDet result[0, 0] = (a[1, 1] * a[2, 2] - a[2, 1] * a[1, 2]) * invDet
result[0, 1] = -(a[0, 1] * a[2, 2] - a[0, 2] * a[2, 1]) * invDet result[0, 1] = -(a[0, 1] * a[2, 2] - a[0, 2] * a[2, 1]) * invDet
result[0, 2] = (a[0, 1] * a[1, 2] - a[0, 2] * a[1, 1]) * invDet result[0, 2] = (a[0, 1] * a[1, 2] - a[0, 2] * a[1, 1]) * invDet
@ -650,69 +628,37 @@ type Mat4* = array[16, float32] ## 4x4 Matrix - OpenGL row order
template `[]`*(a: Mat4, i, j: int): float32 = a[i * 4 + j] template `[]`*(a: Mat4, i, j: int): float32 = a[i * 4 + j]
template `[]=`*(a: Mat4, i, j: int, v: float32) = a[i * 4 + j] = v template `[]=`*(a: Mat4, i, j: int, v: float32) = a[i * 4 + j] = v
proc mat4*(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, proc mat4*(
v14, v15: float32): Mat4 = v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15: float32
result[0] = v0 ): Mat4 {.inline.} =
result[1] = v1 [
result[2] = v2 v0, v1, v2, v3,
result[3] = v3 v4, v5, v6, v7,
result[4] = v4 v8, v9, v10, v11,
result[5] = v5 v12, v13, v14, v15
result[6] = v6 ]
result[7] = v7
result[8] = v8
result[9] = v9
result[10] = v10
result[11] = v11
result[12] = v12
result[13] = v13
result[14] = v14
result[15] = v15
proc mat4*(a: Mat4): Mat4 = proc mat4*(a: Mat4): Mat4 {.inline.} =
a a
proc identity*(): Mat4 = proc identity*(): Mat4 {.inline.} =
result[0] = 1 [
result[1] = 0 1.float32, 0, 0, 0,
result[2] = 0 0, 1, 0, 0,
result[3] = 0 0, 0, 1, 0,
result[4] = 0 0, 0, 0, 1
result[5] = 1 ]
result[6] = 0
result[7] = 0
result[8] = 0
result[9] = 0
result[10] = 1
result[11] = 0
result[12] = 0
result[13] = 0
result[14] = 0
result[15] = 1
proc mat4*(): Mat4 = proc mat4*(): Mat4 {.inline.} =
identity() identity()
proc transpose*(a: Mat4): Mat4 = proc transpose*(a: Mat4): Mat4 {.inline.} =
result[0] = a[0] [
result[1] = a[4] a[0, 0], a[1, 0], a[2, 0], a[3, 0],
result[2] = a[8] a[0, 1], a[1, 1], a[2, 1], a[3, 1],
result[3] = a[12] a[0, 2], a[1, 2], a[2, 2], a[3, 2],
a[0, 3], a[1, 3], a[2, 3], a[3, 3]
result[4] = a[1] ]
result[5] = a[5]
result[6] = a[9]
result[7] = a[13]
result[8] = a[2]
result[9] = a[6]
result[10] = a[10]
result[11] = a[14]
result[12] = a[3]
result[13] = a[7]
result[14] = a[11]
result[15] = a[15]
proc determinant*(a: Mat4): float32 = proc determinant*(a: Mat4): float32 =
var var
@ -850,66 +796,66 @@ proc `*`*(a, b: Mat4): Mat4 =
result[15] = b30*a03 + b31*a13 + b32*a23 + b33*a33 result[15] = b30*a03 + b31*a13 + b32*a23 + b33*a33
proc `*`*(a: Mat4, b: Vec3): Vec3 = proc `*`*(a: Mat4, b: Vec3): Vec3 =
result.x = a[0]*b.x + a[4]*b.y + a[8]*b.z + a[12] result.x = a[0] * b.x + a[4] * b.y + a[8] * b.z + a[12]
result.y = a[1]*b.x + a[5]*b.y + a[9]*b.z + a[13] result.y = a[1] * b.x + a[5] * b.y + a[9] * b.z + a[13]
result.z = a[2]*b.x + a[6]*b.y + a[10]*b.z + a[14] result.z = a[2] * b.x + a[6] * b.y + a[10] * b.z + a[14]
proc `*`*(a: Mat4, b: Vec4): Vec4 = proc `*`*(a: Mat4, b: Vec4): Vec4 =
result.x = a[0]*b.x + a[4]*b.y + a[8]*b.z + a[12]*b.w result.x = a[0] * b.x + a[4] * b.y + a[8] * b.z + a[12] * b.w
result.y = a[1]*b.x + a[5]*b.y + a[9]*b.z + a[13]*b.w result.y = a[1] * b.x + a[5] * b.y + a[9] * b.z + a[13] * b.w
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 {.inline.} =
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]
sqrt(x*x + y*y + z*z) sqrt(x * x + y * y + z * z)
#[ #[
proc translate*(a: Mat4, v: Vec3): Mat4 = proc translate*(a: Mat4, v: Vec3): Mat4 =
@ -986,16 +932,16 @@ 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)
result[0] = (near*2) / rl result[0] = (near * 2) / rl
result[1] = 0 result[1] = 0
result[2] = 0 result[2] = 0
result[3] = 0 result[3] = 0
result[4] = 0 result[4] = 0
result[5] = (near*2) / tb result[5] = (near * 2) / tb
result[6] = 0 result[6] = 0
result[7] = 0 result[7] = 0
result[8] = (right + left) / rl result[8] = (right + left) / rl
@ -1004,17 +950,17 @@ proc frustum*(left, right, bottom, top, near, far: float32): Mat4 =
result[11] = -1 result[11] = -1
result[12] = 0 result[12] = 0
result[13] = 0 result[13] = 0
result[14] = -(far*near*2) / fn result[14] = -(far * near * 2) / fn
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)
@ -1036,7 +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]
@ -1057,34 +1003,34 @@ proc lookAt*(eye, center, up: Vec3): Mat4 =
z2 = eyez - center[2] z2 = eyez - center[2]
# normalize (no check needed for 0 because of early return) # normalize (no check needed for 0 because of early return)
var len = 1/sqrt(z0*z0 + z1*z1 + z2*z2) var len = 1 / sqrt(z0 * z0 + z1 * z1 + z2 * z2)
z0 *= len z0 *= len
z1 *= len z1 *= len
z2 *= len z2 *= len
var var
# vec3.normalize(vec3.cross(up, z, x)) # vec3.normalize(vec3.cross(up, z, x))
x0 = upy*z2 - upz*z1 x0 = upy * z2 - upz * z1
x1 = upz*z0 - upx*z2 x1 = upz * z0 - upx * z2
x2 = upx*z1 - upy*z0 x2 = upx * z1 - upy * z0
len = sqrt(x0*x0 + x1*x1 + x2*x2) len = sqrt(x0 * x0 + x1 * x1 + x2 * x2)
if len == 0: if len == 0:
x0 = 0 x0 = 0
x1 = 0 x1 = 0
x2 = 0 x2 = 0
else: else:
len = 1/len len = 1 / len
x0 *= len x0 *= len
x1 *= len x1 *= len
x2 *= len x2 *= len
var var
# vec3.normalize(vec3.cross(z, x, y)) # vec3.normalize(vec3.cross(z, x, y))
y0 = z1*x2 - z2*x1 y0 = z1 * x2 - z2 * x1
y1 = z2*x0 - z0*x2 y1 = z2 * x0 - z0 * x2
y2 = z0*x1 - z1*x0 y2 = z0 * x1 - z1 * x0
len = sqrt(y0*y0 + y1*y1 + y2*y2) len = sqrt(y0 * y0 + y1 * y1 + y2 * y2)
if len == 0: if len == 0:
y0 = 0 y0 = 0
y1 = 0 y1 = 0
@ -1107,9 +1053,9 @@ proc lookAt*(eye, center, up: Vec3): Mat4 =
result[9] = y2 result[9] = y2
result[10] = z2 result[10] = z2
result[11] = 0 result[11] = 0
result[12] = -(x0*eyex + x1*eyey + x2*eyez) result[12] = -(x0 * eyex + x1 * eyey + x2 * eyez)
result[13] = -(y0*eyex + y1*eyey + y2*eyez) result[13] = -(y0 * eyex + y1 * eyey + y2 * eyez)
result[14] = -(z0*eyex + z1*eyey + z2*eyez) result[14] = -(z0 * eyex + z1 * eyey + z2 * eyez)
result[15] = 1 result[15] = 1
proc mat3*(m: Mat4): Mat3 = proc mat3*(m: Mat4): Mat3 =
@ -1182,19 +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 +
@ -1209,23 +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
@ -1249,16 +1195,29 @@ 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
result.z = q.z * v result.z = q.z * v
result.w = q.w * v result.w = q.w * v
proc `/`*(q: Quat, v: float32): Quat {.inline.} =
## Divide the quaternion by a float32.
result.x = q.x / v
result.y = q.y / v
result.z = q.z / v
result.w = q.w / v
proc `*=`*(a: var Quat, b: float32) {.inline.} =
a = a * b
proc `/=`*(a: var Quat, b: float32) {.inline.} =
a = a / b
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
@ -1277,29 +1236,35 @@ 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)
@ -1312,17 +1277,18 @@ 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)
@ -1342,11 +1308,11 @@ 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]
@ -1359,8 +1325,9 @@ 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:
@ -1382,8 +1349,9 @@ 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
@ -1402,18 +1370,19 @@ 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 =
@ -1434,8 +1403,8 @@ 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 =
if dot(a, b) < 0: if dot(a, b) < 0:
@ -1447,25 +1416,25 @@ 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

16
tests/test.nim
View file

@ -1,5 +1,21 @@
import vmath, osproc, random, streams import vmath, osproc, random, streams
var v2 = vec2(0, 0)
v2 *= 1
v2 /= 1
var v3 = vec3(0, 0, 0)
v3 *= 1
v3 /= 1
var v4 = vec4(0, 0, 0, 0)
v4 *= 1
v4 /= 1
var q = quat(0, 0, 0, 0)
q *= 1
q /= 1
var s = newFileStream("tests/test-output.txt", fmWrite) var s = newFileStream("tests/test-output.txt", fmWrite)
randomize(1234) randomize(1234)