365 lines
9.2 KiB
Lua
365 lines
9.2 KiB
Lua
--- A 3 component vector.
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-- @module vec3
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local sqrt = math.sqrt
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local cos = math.cos
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local sin = math.sin
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local vec3 = {}
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local vec3_mt = {}
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-- Private constructor.
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local function new(x, y, z)
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local v = {}
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v.x, v.y, v.z = x, y, z
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return setmetatable(v, vec3_mt)
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end
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-- Do the check to see if JIT is enabled. If so use the optimized FFI structs.
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local status, ffi
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if type(jit) == "table" and jit.status() then
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status, ffi = pcall(require, "ffi")
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if status then
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ffi.cdef "typedef struct { double x, y, z;} cpml_vec3;"
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new = ffi.typeof("cpml_vec3")
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end
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end
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--- Constants
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-- @table vec3
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-- @field unit_x X axis of rotation
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-- @field unit_y Y axis of rotation
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-- @field unit_z Z axis of rotation
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-- @field zero Empty vector
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vec3.unit_x = new(1, 0, 0)
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vec3.unit_y = new(0, 1, 0)
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vec3.unit_z = new(0, 0, 1)
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vec3.zero = new(0, 0, 0)
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-- Statically allocate a temporary variable used in some of our functions.
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local tmp = new(0, 0, 0)
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--- The public constructor.
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-- @param x Can be of three types: </br>
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-- number X component
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-- table {x, y, z} or {x=x, y=y, z=z}
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-- scalar To fill the vector eg. {x, x, x}
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-- @tparam number y Y component
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-- @tparam number z Z component
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-- @treturn vec3 out
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function vec3.new(x, y, z)
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-- number, number, number
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if x and y and z then
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assert(type(x) == "number", "new: Wrong argument type for x (<number> expected)")
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assert(type(y) == "number", "new: Wrong argument type for y (<number> expected)")
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assert(type(z) == "number", "new: Wrong argument type for z (<number> expected)")
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return new(x, y, z)
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-- {x, y, z} or {x=x, y=y, z=z}
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elseif type(x) == "table" then
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local x, y, z = x.x or x[1], x.y or x[2], x.z or x[3]
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assert(type(x) == "number", "new: Wrong argument type for x (<number> expected)")
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assert(type(y) == "number", "new: Wrong argument type for y (<number> expected)")
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assert(type(z) == "number", "new: Wrong argument type for z (<number> expected)")
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return new(x, y, z)
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-- number
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elseif type(x) == "number" then
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return new(x, x, x)
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else
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return new(0, 0, 0)
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end
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end
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--- Clone a vector.
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-- @tparam vec3 a Vector to be cloned
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-- @treturn vec3 out
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function vec3.clone(a)
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return new(a.x, a.y, a.z)
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end
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--- Add two vectors.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn vec3 out
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function vec3.add(out, a, b)
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out.x = a.x + b.x
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out.y = a.y + b.y
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out.z = a.z + b.z
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return out
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end
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--- Subtract one vector from another.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn vec3 out
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function vec3.sub(out, a, b)
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out.x = a.x - b.x
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out.y = a.y - b.y
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out.z = a.z - b.z
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return out
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end
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--- Multiply a vector by another vectorr.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn vec3 out
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function vec3.mul(out, a, b)
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out.x = a.x * b.x
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out.y = a.y * b.y
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out.z = a.z * b.z
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return out
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end
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--- Divide a vector by a scalar.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn vec3 out
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function vec3.div(out, a, b)
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out.x = a.x / b.x
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out.y = a.y / b.y
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out.z = a.z / b.z
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return out
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end
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--- Get the normal of a vector.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Vector to normalize
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-- @treturn vec3 out
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function vec3.normalize(out, a)
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local l = vec3.len(a)
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out.x = a.x / l
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out.y = a.y / l
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out.z = a.z / l
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return out
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end
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--- Trim a vector to a given length
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Vector to be trimmed
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-- @tparam number len Length to trim the vector to
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-- @treturn vec3 out
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function vec3.trim(out, a, len)
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return out
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:normalize(a)
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:scale(out, math.min(vec3.len(a), len))
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end
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--- Get the cross product of two vectors.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn vec3 out
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function vec3.cross(out, a, b)
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out.x = a.y * b.z - a.z * b.y
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out.y = a.z * b.x - a.x * b.z
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out.z = a.x * b.y - a.y * b.x
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return out
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end
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--- Get the dot product of two vectors.
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn number dot
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function vec3.dot(a, b)
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return a.x * b.x + a.y * b.y + a.z * b.z
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end
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--- Get the length of a vector.
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-- @tparam vec3 a Vector to get the length of
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-- @treturn number len
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function vec3.len(a)
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return sqrt(a.x * a.x + a.y * a.y + a.z * a.z)
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end
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--- Get the squared length of a vector.
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-- @tparam vec3 a Vector to get the squared length of
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-- @treturn number len
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function vec3.len2(a)
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return a.x * a.x + a.y * a.y + a.z * a.z
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end
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--- Get the distance between two vectors.
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn number dist
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function vec3.dist(a, b)
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local dx = a.x - b.x
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local dy = a.y - b.y
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local dz = a.z - b.z
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return sqrt(dx * dx + dy * dy + dz * dz)
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end
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--- Get the squared distance between two vectors.
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @treturn number dist
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function vec3.dist2(a, b)
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local dx = a.x - b.x
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local dy = a.y - b.y
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local dz = a.z - b.z
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return dx * dx + dy * dy + dz * dz
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end
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--- Scale a vector by a scalar.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam number b Right hand operant
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-- @treturn vec3 out
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function vec3.scale(out, a, b)
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out.x = a.x * b
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out.y = a.y * b
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out.z = a.z * b
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return out
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end
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--- Rotate vector about an axis.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Vector to rotate
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-- @tparam number phi Amount to rotate, in radians
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-- @tparam vec3 axis Axis to rotate by
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-- @treturn vec3 out
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function vec3.rotate(out, a, phi, axis)
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if not vec3.is_vec3(axis) then
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return a
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end
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local u = new():normalize(axis)
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local c = cos(phi)
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local s = sin(phi)
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-- Calculate generalized rotation matrix
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local m1 = new((c + u.x * u.x * (1 - c)), (u.x * u.y * (1 - c) - u.z * s), (u.x * u.z * (1 - c) + u.y * s))
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local m2 = new((u.y * u.x * (1 - c) + u.z * s), (c + u.y * u.y * (1 - c)), (u.y * u.z * (1 - c) - u.x * s))
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local m3 = new((u.z * u.x * (1 - c) - u.y * s), (u.z * u.y * (1 - c) + u.x * s), (c + u.z * u.z * (1 - c)) )
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out.x = a:dot(m1)
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out.y = a:dot(m2)
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out.z = a:dot(m3)
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return out
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end
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function vec3.perpendicular(out, a)
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out.x = -a.y
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out.y = a.x
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out.z = 0
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return out
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end
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--- Lerp between two vectors.
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-- @tparam vec3 out Vector to store the result
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-- @tparam vec3 a Left hand operant
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-- @tparam vec3 b Right hand operant
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-- @tparam number s Step value
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-- @treturn vec3 out
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function vec3.lerp(out, a, b, s)
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return out
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:sub(b, a)
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:scale(out, s)
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:add(out, a)
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end
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--- Unpack a vector into individual components.
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-- @tparam vec3 a Vector to unpack
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-- @treturn number x
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-- @treturn number y
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-- @treturn number z
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function vec3.unpack(a)
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return a.x, a.y, a.z
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end
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--- Return a boolean showing if a table is or is not a vec3.
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-- @tparam vec3 a Vector to be tested
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-- @treturn boolean is_vec3
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function vec3.is_vec3(a)
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if type(a) == "cdata" then
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return ffi.istype("cpml_vec3", a)
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end
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return
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type(a) == "table" and
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type(a.x) == "number" and
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type(a.y) == "number" and
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type(a.z) == "number"
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end
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--- Return a boolean showing if a table is or is not a zero vec3.
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-- @tparam vec3 a Vector to be tested
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-- @treturn boolean is_zero
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function vec3.is_zero(a)
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return
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a.x == 0 and
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a.y == 0 and
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a.z == 0
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end
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--- Return a formatted string.
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-- @tparam vec3 a Vector to be turned into a string
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-- @treturn string formatted
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function vec3.to_string(a)
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return string.format("(%+0.3f,%+0.3f,%+0.3f)", a.x, a.y, a.z)
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end
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vec3_mt.__index = vec3
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vec3_mt.__tostring = vec3.to_string
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function vec3_mt.__call(_, x, y, z)
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return vec3.new(x, y, z)
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end
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function vec3_mt.__unm(a)
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return new(-a.x, -a.y, -a.z)
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end
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function vec3_mt.__eq(a, b)
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if not vec3.is_vec3(a) or not vec3.is_vec3(b) then
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return false
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end
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return a.x == b.x and a.y == b.y and a.z == b.z
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end
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function vec3_mt.__add(a, b)
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assert(vec3.is_vec3(a), "__add: Wrong argument type for left hand operant. (<cpml.vec3> expected)")
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assert(vec3.is_vec3(b), "__add: Wrong argument type for right hand operant. (<cpml.vec3> expected)")
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return new():add(a, b)
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end
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function vec3_mt.__sub(a, b)
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assert(vec3.is_vec3(a), "__sub: Wrong argument type for left hand operant. (<cpml.vec3> expected)")
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assert(vec3.is_vec3(b), "__sub: Wrong argument type for right hand operant. (<cpml.vec3> expected)")
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return new():sub(a, b)
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end
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function vec3_mt.__mul(a, b)
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assert(vec3.is_vec3(a), "__mul: Wrong argument type for left hand operant. (<cpml.vec3> expected)")
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assert(vec3.is_vec3(b) or type(b) == "number", "__mul: Wrong argument type for right hand operant. (<cpml.vec3> or <number> expected)")
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if vec3.is_vec3(b) then
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return new():mul(a, b)
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end
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return new():scale(a, b)
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end
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function vec3_mt.__div(a, b)
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assert(vec3.is_vec3(a), "__div: Wrong argument type for left hand operant. (<cpml.vec3> expected)")
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assert(vec3.is_vec3(b) or type(b) == "number", "__div: Wrong argument type for right hand operant. (<cpml.vec3> or <number> expected)")
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if vec3.is_vec3(b) then
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return new():div(a, b)
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end
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return new():scale(a, 1 / b)
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end
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if status then
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ffi.metatype(new, vec3_mt)
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end
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return setmetatable({}, vec3_mt)
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