I have a problem converting Heading, Pitch and Roll to an Orientation Matrix

How would I go about improving this to ensure Y and Z and are correctly calculated.

--[[
  get_orientation - Returns the orientation matrix of an object based on its heading, pitch, and roll in degrees.
  
  @param heading number - The heading of the object in degrees.
  @param pitch number - The pitch of the object in degrees.
  @param roll number - The roll of the object in degrees.
  @returns orientation table - The orientation matrix of the object, represented as a table with three unit vectors: x, y, and z.
]]
local function get_orientation(heading, pitch, roll)
    local orientation = {}

    -- Convert the heading, pitch, and roll from degrees to radians using math.rad
    heading = math.rad(heading)
    pitch = math.rad(pitch)
    roll = math.rad(roll)

    -- Calculate the x unit vector
    -- x is the Vec3 unit vector that points in the direction of the object's front
    orientation.x = {}
    orientation.x.x = math.cos(heading) * math.cos(pitch)
    orientation.x.y = math.sin(pitch)
    orientation.x.z = math.sin(heading) * math.cos(pitch)

    -- Calculate the y unit vector
    -- y is the Vec3 unit vector that points in the direction of the object's top
    orientation.y = {}
    orientation.y.x = -math.cos(heading) * math.sin(pitch)
    orientation.y.y = math.cos(pitch)
    orientation.y.z = -math.sin(heading) * math.sin(pitch)

    -- Calculate the z unit vector
    -- z is the Vec3 unit vector that points in the direction of the object's right side
    orientation.z = {}
    orientation.z.x = -math.sin(heading)
    orientation.z.z = -math.cos(heading) * math.cos(roll)
    orientation.z.y = math.sin(roll)

    -- Return the orientation matrix of the object
    return orientation
end

---------------------------------------------------
---------------------------------------------------
local lat = 41.610278
local lon = 41.599444
local heading = 90
local pitch = 25
local roll = 0
local alt = 100


local x, y = terrain.convertLatLonToMeters(lat, lon)

local orientation = get_orientation(heading, pitch, roll)

local position = {
    x=orientation.x,
    y=orientation.y,
    z=orientation.z,
    p={x=x,y=alt,z=y}
}

Export.LoSetCameraPosition(position)
local actual = Export.LoGetCameraPosition()

return {position=position, actual=actual}

There is a little more information about the Orientation here https://www.digitalcombatsimulator.com/en/support/faq/1256/#:~:text=level 10 m-,Orientation,-Object orientation is

I am attempting to build a function that takes lat, lon, alt, heading, pitch and roll and produce the Position matrix.

I have the example function so far, which does work but everything goes funky after -81 pitch and the roll does not work as intended.

CodePudding user response：

Formulas for 3D rotation are not simple, but they can be simply deduced from three consecutive 2D rotations.

local function apply_rotation(a, b, angle)
   local ax, ay, az, bx, by, bz = a.x, a.y, a.z, b.x, b.y, b.z
   a.x = math.cos(angle) * ax   math.sin(angle) * bx
   a.y = math.cos(angle) * ay   math.sin(angle) * by
   a.z = math.cos(angle) * az   math.sin(angle) * bz
   b.x = math.cos(angle) * bx - math.sin(angle) * ax
   b.y = math.cos(angle) * by - math.sin(angle) * ay
   b.z = math.cos(angle) * bz - math.sin(angle) * az
end

local function get_orientation(heading, pitch, roll)

    -- Convert the heading, pitch, and roll from degrees to radians using math.rad
    heading = math.rad(heading)
    pitch = math.rad(pitch)
    roll = math.rad(roll)

    -- x is the Vec3 unit vector that points in the direction of the object's front
    -- y is the Vec3 unit vector that points in the direction of the object's top
    -- z is the Vec3 unit vector that points in the direction of the object's right side
    local o = {
        x = { x=1, y=0, z=0 },
        y = { x=0, y=1, z=0 },
        z = { x=0, y=0, z=1 },
    }

    apply_rotation(o.x, o.z, heading)
    apply_rotation(o.x, o.y, pitch)
    apply_rotation(o.z, o.y, roll)

    -- Return the orientation matrix of the object
    return o
end