/
revolute-joint.sml
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/
revolute-joint.sml
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structure BDDRevoluteJoint =
struct
open BDDTypes
open BDDMath
open BDDOps
infix 6 :+: :-: %-% %+% +++
infix 7 *: *% +*: +*+ #*% @*:
structure D = BDDDynamics
exception RevoluteJoint of string
(* Put this here for now.
Later, I think we're just going to put everything in joint.sml.
*)
datatype limit_state = InactiveLimit
| AtLowerLimit
| AtUpperLimit
| EqualLimits
fun assert (b : bool) =
if b then () else raise RevoluteJoint "assertion failed"
fun new {local_anchor_a : vec2,
local_anchor_b : vec2,
reference_angle : real,
lower_angle : real,
upper_angle : real,
max_motor_torque : real,
motor_speed : real,
enable_limit : bool,
enable_motor : bool
}
joint =
let
val bA = D.J.get_body_a joint
val bB = D.J.get_body_b joint
val m_indexA = ref 0
val m_indexB = ref 0
val m_local_anchor_a = local_anchor_a
val m_local_anchor_b = local_anchor_b
val m_local_center_a = ref (vec2 (0.0, 0.0))
val m_local_center_b = ref (vec2 (0.0, 0.0))
val m_invMassA = ref 0.0
val m_invMassB = ref 0.0
val m_invIA = ref 0.0
val m_invIB = ref 0.0
val m_reference_angle = reference_angle
val m_impulse = ref (vec3 (0.0, 0.0, 0.0))
val m_motor_impulse = ref 0.0
val m_lower_angle = ref lower_angle
val m_upper_angle = ref upper_angle
val m_max_motor_torque = max_motor_torque
val m_motor_speed = ref motor_speed
val m_enable_limit = ref enable_limit
val m_enable_motor = ref enable_motor
val m_limit_state = ref InactiveLimit
val m_mass = ref (mat33with (0.0, 0.0, 0.0,
0.0, 0.0, 0.0,
0.0, 0.0, 0.0))
val m_motor_mass = ref 0.0
val m_rA = ref (vec2 (0.0, 0.0))
val m_rB = ref (vec2 (0.0, 0.0))
fun init_velocity_constraints { step : BDDDynamicsTypes.time_step,
positionsc,
positionsa,
velocitiesv,
velocitiesw } =
let
val () = m_indexA := D.B.get_island_index bA
val () = m_indexB := D.B.get_island_index bB
val () = m_local_center_a := sweeplocalcenter (D.B.get_sweep bA)
val () = m_local_center_b := sweeplocalcenter (D.B.get_sweep bB)
val () = m_invMassA := D.B.get_inv_mass bA
val () = m_invMassB := D.B.get_inv_mass bB
val () = m_invIA := D.B.get_inv_i bA
val () = m_invIB := D.B.get_inv_i bB
val aA = Array.sub(positionsa, !m_indexA)
val aB = Array.sub(positionsa, !m_indexB)
val qA = mat22angle aA
val qB = mat22angle aB
val () = m_rA := qA +*: (m_local_anchor_a :-: !m_local_center_a)
val () = m_rB := qB +*: (m_local_anchor_b :-: !m_local_center_b)
(* J = [-I -r1_skew I r2_skew]
[ 0 -1 0 1]
r_skew = [-ry; rx] *)
(* K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
[ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
[ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB] *)
val mA = !m_invMassA
val mB = !m_invMassB
val iA = !m_invIA
val iB = !m_invIB
val (rax, ray) = vec2xy (!m_rA)
val (rbx, rby) = vec2xy (!m_rB)
val eyx = ~ray * rax * iA - rby * rbx * iB
val ezx = ~ray * iA - rby * iB
val ezy = rax * iA + rbx * iB
val () = m_mass :=
(mat33with (mA + mB + ray * ray * iA + rby * rby * iB,
eyx,
ezx,
eyx,
mA + mB + rax * rax * iA + rbx * rbx * iB,
ezy,
ezx,
ezy,
iA + iB
))
val () = m_motor_mass := iA + iB
val () = if !m_motor_mass > 0.0
then m_motor_mass := 1.0 / !m_motor_mass
else ()
val () = if !m_enable_motor = false (* or fixed_rotation? *)
then m_motor_impulse := 0.0
else ()
val () = if !m_enable_limit (* and fixed_rotation = false? *)
then let val joint_angle = aB - aA - m_reference_angle
val (ix, iy) = (vec3x (!m_impulse), vec3y (!m_impulse))
val () = if abs (!m_upper_angle - !m_lower_angle)
< 2.0 * BDDSettings.angular_slop
then m_limit_state := EqualLimits
else if joint_angle <= !m_lower_angle
then (if !m_limit_state <> AtLowerLimit
then m_impulse := vec3 (ix, iy, 0.0)
else ();
m_limit_state := AtLowerLimit
)
else if joint_angle >= !m_upper_angle
then (if !m_limit_state <> AtUpperLimit
then m_impulse := vec3 (ix, iy, 0.0)
else ();
m_limit_state := AtUpperLimit
)
else (m_limit_state := InactiveLimit;
m_impulse := vec3 (ix, iy, 0.0))
in () end
else m_limit_state := InactiveLimit
val () = if #warm_starting step
then let
val dt_ratio = #dt_ratio step
(* Scale impulses to support a variable time step. *)
val () = m_impulse := dt_ratio *% !m_impulse
val () = m_motor_impulse := !m_motor_impulse * dt_ratio;
val p = vec2 (vec3x (!m_impulse), vec3y (!m_impulse))
val () = Array.update
(velocitiesv, !m_indexA,
Array.sub(velocitiesv, !m_indexA) :-: mA *: p)
val () = Array.update
(velocitiesw, !m_indexA,
(Array.sub(velocitiesw, !m_indexA)) -
iA * (cross2vv (!m_rA, p) + !m_motor_impulse
+ (vec3z (!m_impulse))))
val () = Array.update
(velocitiesv, !m_indexB,
Array.sub(velocitiesv, !m_indexB) :+: mB *: p)
val () = Array.update
(velocitiesw, !m_indexB,
Array.sub(velocitiesw, !m_indexB) +
iB * (cross2vv (!m_rB, p) + !m_motor_impulse
+ (vec3z (!m_impulse))))
in () end
else (m_impulse := vec3 (0.0, 0.0, 0.0);
m_motor_impulse := 0.0)
in ()
end
fun solve_velocity_constraints { step : BDDDynamicsTypes.time_step,
positionsc,
positionsa,
velocitiesv,
velocitiesw } =
let
val vA = ref (Array.sub(velocitiesv, !m_indexA))
val wA = ref (Array.sub(velocitiesw, !m_indexA))
val vB = ref (Array.sub(velocitiesv, !m_indexB))
val wB = ref (Array.sub(velocitiesw, !m_indexB))
val mA = !m_invMassA
val mB = !m_invMassB
val iA = !m_invIA
val iB = !m_invIB
(*bool fixedRotation = (iA + iB == 0.0f); *)
(* Solve motor constraint *)
val () = if (!m_enable_motor andalso !m_limit_state <> EqualLimits)
then
let val Cdot = !wB - !wA - !m_motor_speed
val impulse = ~(!m_motor_mass) * Cdot
val old_impulse = !m_motor_impulse
val max_impulse = (#dt step) * m_max_motor_torque
val () = m_motor_impulse :=
clampr (!m_motor_impulse + impulse,
~max_impulse,
max_impulse)
val impulse = !m_motor_impulse - old_impulse
val () = wA := !wA - iA * impulse
val () = wB := !wB + iB * impulse
in () end
else ()
(* Solve limit constraint. *)
val () = if !m_enable_limit andalso !m_limit_state <> InactiveLimit
then
let val Cdot1 = !vB :+: cross2sv (!wB, !m_rB)
:-: !vA :-: cross2sv (!wA, !m_rA)
val Cdot2 = !wB - !wA
val Cdot = vec3 (vec2x Cdot1, vec2y Cdot1, Cdot2)
val impulse = ref (~1.0 *% mat33solve33 (!m_mass, Cdot))
fun update_impulses cond =
if cond
then let
(* 2010 Box2D only has -Cdot1 here *)
val rhs =
(~1.0) *: Cdot1 :+:
vec3z (!m_impulse) *:
vec2(vec3x (mat33col3 (!m_mass)),
vec3y (mat33col3 (!m_mass))
)
val reduced = mat33solve22 (!m_mass, rhs)
val () = impulse :=
vec3 (vec2x reduced,
vec2y reduced,
~ (vec3z (!m_impulse)))
val () = m_impulse :=
vec3 (vec3x (!m_impulse) +
vec2x reduced,
vec3y (!m_impulse) +
vec2y reduced,
0.0)
in () end
else m_impulse := !m_impulse %+% !impulse
val () =
case !m_limit_state of
EqualLimits =>
m_impulse := !m_impulse %+% !impulse
| AtLowerLimit =>
update_impulses
(vec3z (!m_impulse) + vec3z (!impulse) < 0.0)
| AtUpperLimit =>
update_impulses
(vec3z (!m_impulse) + vec3z (!impulse) > 0.0)
| _ => ()
val P = vec2 (vec3x (!impulse), vec3y (!impulse))
val () = vA := !vA :-: mA *: P
val () = wA := !wA - iA *
(cross2vv (!m_rA, P) + vec3z (!impulse))
val () = vB := !vB :+: mB *: P
val () = wB := !wB + iB *
(cross2vv (!m_rB, P) + vec3z (!impulse))
in () end
else
(* Solve point-to-point constraint *)
let val Cdot = !vB :+: cross2sv (!wB, !m_rB)
:-: !vA :-: cross2sv (!wA, !m_rA)
val impulse = mat33solve22 (!m_mass, ~1.0 *: Cdot)
val () = m_impulse :=
vec3 (vec3x (!m_impulse) + vec2x impulse,
vec3y (!m_impulse) + vec2y impulse,
vec3z (!m_impulse))
val () = vA := !vA :-: mA *: impulse
val () = wA := !wA - iA *
(cross2vv (!m_rA, impulse))
val () = vB := !vB :+: mB *: impulse
val () = wB := !wB + iB *
(cross2vv (!m_rB, impulse))
in () end
in Array.update (velocitiesv, !m_indexA, !vA);
Array.update (velocitiesw, !m_indexA, !wA);
Array.update (velocitiesv, !m_indexB, !vB);
Array.update (velocitiesw, !m_indexB, !wB)
end
fun solve_position_constraints { step,
positionsc,
positionsa,
velocitiesv,
velocitiesw } =
let
val aA = ref (Array.sub(positionsa, !m_indexA))
val cA = ref (Array.sub(positionsc, !m_indexA))
val aB = ref (Array.sub(positionsa, !m_indexB))
val cB = ref (Array.sub(positionsc, !m_indexB))
val iA = !m_invIA
val iB = !m_invIB
val angularError = ref 0.0
(* Solve angular limit constraint. *)
val () =
if !m_enable_limit andalso !m_limit_state <> InactiveLimit
then let val angle = !aB - !aA - m_reference_angle
val limitImpulse =
case !m_limit_state of
EqualLimits =>
let (* Prevent large angular correction *)
val C = clampr (angle - !m_lower_angle,
~BDDSettings.max_angular_correction,
BDDSettings.max_angular_correction)
val () = angularError := abs C
in ~(!m_motor_mass) * C end
| AtLowerLimit =>
let
val C = angle - !m_lower_angle
val () = angularError := ~C
(* Prevent large angular corrections and allow
some slop. *)
val C1 = clampr (C + BDDSettings.angular_slop,
~BDDSettings.max_angular_correction,
0.0)
in ~(!m_motor_mass) * C1 end
| AtUpperLimit =>
let
val C = angle - !m_upper_angle
val () = angularError := C
(* Prevent large angular corrections and allow
some slop. *)
val C1 = clampr (C - BDDSettings.angular_slop,
0.0,
BDDSettings.max_angular_correction)
in ~(!m_motor_mass) * C1 end
| _ => 0.0
val () = aA := !aA - iA * limitImpulse
val () = aB := !aB + iB * limitImpulse
in () end
else ()
(* Solve point-to-point constraint. *)
val qA = mat22angle (!aA)
val qB = mat22angle (!aB)
val rA = qA +*: (m_local_anchor_a :-: !m_local_center_a)
val rB = qB +*: (m_local_anchor_b :-: !m_local_center_b)
val C = !cB :+: rB :-: !cA :-: rA
val positionError = vec2length C
val mA = D.B.get_inv_mass bA
val mB = D.B.get_inv_mass bB
val (rax, ray) = vec2xy rA
val (rbx, rby) = vec2xy rB
val K = mat22with
(mA + mB + iA * ray * ray + iB * rby * rby,
~iA * rax * ray - iB * rbx * rby,
~iA * rax * ray - iB * rbx * rby,
mA + mB + iA * rax * rax + iB * rbx * rbx
)
val impulse = ~1.0 *: mat22solve (K, C)
val () = cA := !cA :-: mA *: impulse
val () = aA := !aA - iA * cross2vv (rA, impulse)
val () = cB := !cB :+: mB *: impulse
val () = aB := !aB + iB * cross2vv (rB, impulse)
val () = Array.update(positionsa, !m_indexA, !aA)
val () = Array.update(positionsa, !m_indexB, !aB)
val () = Array.update(positionsc, !m_indexA, !cA)
val () = Array.update(positionsc, !m_indexB, !cB)
in positionError <= BDDSettings.linear_slop andalso
!angularError <= BDDSettings.angular_slop
end
fun get_anchor_a () = D.B.get_world_point (bA, m_local_anchor_a)
fun get_anchor_b () = D.B.get_world_point (bB, m_local_anchor_b)
fun enable_limit flag =
if flag <> !m_enable_limit
then (D.B.set_awake (bA, true);
D.B.set_awake (bB, true);
m_enable_limit := flag;
m_impulse := vec3 (vec3x (!m_impulse),
vec3y (!m_impulse),
0.0)
)
else ()
fun is_limit_enabled () = !m_enable_limit
fun enable_motor flag =
(D.B.set_awake (bA, true);
D.B.set_awake (bB, true);
m_enable_motor := flag
)
fun is_motor_enabled () = !m_enable_motor
val dispatch =
{
init_velocity_constraints = init_velocity_constraints,
solve_velocity_constraints = solve_velocity_constraints,
solve_position_constraints = solve_position_constraints,
get_anchor_a = get_anchor_a,
get_anchor_b = get_anchor_b
}
val methods = BDDDynamicsTypes.Revolute {enable_limit = enable_limit,
is_limit_enabled = is_limit_enabled,
enable_motor = enable_motor,
is_motor_enabled = is_motor_enabled}
in
(dispatch, methods)
end
end