use <linalg.scad>
use <se3.scad>

function left_multiply(a,bs,i_=0) = i_ >= len(bs) ? [] :
	concat([
		a * bs[i_]
	], left_multiply(a,bs,i_+1));


function right_multiply(as,b,i_=0) = i_ >= len(as) ? [] :
	concat([
		as[i_] * b
	], right_multiply(as,b,i_+1));

function quantize_trajectory(trajectory,step=undef,start_position=0,steps=undef,i_=0,length_=undef) =
	length_ == undef ? quantize_trajectory(
		trajectory=trajectory,
		start_position=(step==undef?norm(take3(trajectory))/steps*start_position:start_position),
		length_=norm(take3(trajectory)),
		step=step,steps=steps,i_=i_) :
	(steps==undef?start_position > length_:i_>=steps) ? [] :
	concat([
	// if steps is defined, ignore start_position
		se3_exp(trajectory*(steps==undef ? start_position/length_
                                         : i_/(steps>1?steps-1:1)))
	], quantize_trajectory(trajectory=trajectory,step=step,start_position=(steps==undef?start_position+step:start_position),steps=steps,i_=i_+1,length_=length_));

function close_trajectory_loop(trajectories) = concat(trajectories,[se3_ln(invert_rt(trajectories_end_position(trajectories)))]);

function quantize_trajectories(trajectories,step=undef,start_position=0,steps=undef,loop=false,last_=identity4(),i_=0,current_length_=undef,j_=0) =
		// due to quantization differences, the last step may be missed. In that case, add it:
	loop==true ? quantize_trajectories(
		trajectories=close_trajectory_loop(trajectories),
		step=step,
		start_position = start_position,
		steps=steps,
		loop=false,
		last_=last_,
		i_=i_,
		current_length_=current_length_,
		j_=j_) :
	i_ >= len(trajectories) ? (j_ < steps ? [last_] : []) :
	current_length_ == undef ? 
	quantize_trajectories(
		trajectories=trajectories,
		step = (step == undef ? trajectories_length(trajectories) / steps : step),
		start_position = (step == undef ? start_position * trajectories_length(trajectories) / steps : start_position),
		steps=steps,
		loop=loop,
		last_=last_,
		i_=i_,
		current_length_=norm(take3(trajectories[i_])),
		j_=j_) :
	concat(
		left_multiply(last_,quantize_trajectory(
			trajectory=trajectories[i_],
			start_position=start_position,
			step=step)),
	quantize_trajectories(
		trajectories=trajectories,
		step=step,
		start_position = start_position > current_length_
			? start_position - current_length_
			: step - ((current_length_-start_position) % step),
		steps=steps,
		loop=loop,
	    last_=last_ * se3_exp(trajectories[i_]),
	    i_=i_+1,
		current_length_ = undef,
		j_=j_+len(

		quantize_trajectory(
			trajectory=trajectories[i_],
			start_position=start_position,
			step=step	

		))
	))
;


function trajectories_length(trajectories, i_=0) = i_ >= len(trajectories) ? 0 
	: norm(take3(trajectories[i_])) + trajectories_length(trajectories,i_+1);


function trajectories_end_position(rt,i_=0,last_=identity4()) = 
	i_ >= len(rt) ? last_ :
	trajectories_end_position(rt, i_+1, last_ * se3_exp(rt[i_]));