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solve_paff_multibeam.m
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% simulate a piece of mask by multiple beams of particle trajectory
figno = 11;
leftB = -150;
rightB = 150;
bottomB = -150;
topB = 150;
% define the boundary boxes
% [dim1a, dim1b; dim2a, dim2b];
g.boundary.box = [leftB, rightB; bottomB, topB];
g.boundary.s = 2;
[X, Y] = meshgrid(leftB:1:rightB, bottomB:1:topB);
% test on the Gaussian smoothing for velocity field
% this is used for decreasing from boundaries
g.vfield_smooth_sigma = 0.1;
% g.s2 is to combine weight
g.s2 = 1;
g = get_control_point_and_transform_multibeam_Lshape(g);
nb_cps = g.nb_cps;
cps = g.cps;
dim = g.dim;
% two collision boundaries
% r1 = intra-beam collision, r1 \approx 1
% r2 = inter-beam collision, r2 can be fairly big, like 10^2 or 20^2
% r is the collision boundary
r1 = 1;
g.r1 = 1;
r2 = 2250; %225;
g.r2 = r2;
% dv is the difference of the velocity when conflicted
g.dv = 1;
% precompute the decreasing ratio
% compute the alpha decresing ratio from trajectory
g.h = 3; % h is the sampling radius of the points in the mask
g.sigma2 = 25; % local decreasing sigma outside of all trajectory
g.sigma1 = 100; % the sigma to combine affine fields, need to be smaller than collision radius
% solve iniitial ode on p and q
% pqhat0 = [p; q];
cpshat0 = reshape(cps, [nb_cps*dim, 1]);
tlist = 0:0.01:1;
if 0
% use ode to solve trajectory and define velocity
[T, cpshat] = ode45(@(t, y) vhat_paff_multibeam(g, t, y), tlist, cpshat0);
nb_T = length(T);
cpslist = reshape(cpshat, [nb_T, dim, nb_cps]); % [pqhat(:, 3), pqhat(:, 4)];
g.nb_T = nb_T;
% recompute the velocity at each point
% cpslist: nb_pts * nb_dim * nb_cps (idx_point, u/v, idx_cps)
cpslist1 = permute(cpslist, [2, 1, 3]);
cpslist2 = repmat(cpslist1, [1, nb_cps, 1]);
vcpslist1 = v_paff_ex_pqvec_multibeam(g, nan, reshape(cpslist1, [dim, nb_T*nb_cps]), cpslist2);
vcpslist = reshape(vcpslist1, [dim, nb_T, nb_cps]);
vcpslist = permute(vcpslist, [2, 1, 3]);
else
% use predefined trjactories, assuming they won't conflict
tlist = 0:0.05:1;
[cpslist, vcpslist] = predefine_trajectory_multibeam(g, tlist);
g.nb_T = length(tlist);
% create a cpslist of extended time duration, with t > 1, to "dilate" the
% trajector mask in the time
tlist_ex = [tlist, 1.05:0.05:1.1];
[cpslist_ex, vcpslist_ex] = predefine_trajectory_multibeam(g, tlist_ex);
% create the long-time mask (from t=0:1, or even extended, t=-0.2:1.2)
mask_longtime_label_ex = scatter_multiple_label_trajectory_after_distance_transform(g, cpslist_ex(:, :, :));
mask_longtime_ex = (mask_longtime_label_ex > 0);
end;
clist = collision_detection_conflicted_velocity_multibeam(g, cpslist, vcpslist);
clist_ex = collision_detection_conflicted_velocity_multibeam(g, cpslist_ex, vcpslist_ex);
disp 'collision time points'
clist
disp 'collision extended time points'
clist_ex
xfield_0 = cat(3, X, Y);
yfield_current = xfield_0;
cpspiecelist = zeros(length(clist), 2, nb_cps);
% qslist = zeros(length(clist)-1, 2);
for ii = 1:nb_cps
cpspiecelist(1, :, ii) = cps(:, ii)';
end;
% cpslist1 = permute(cpslist, [1,3,2]);
% cpslist1 = reshape(cpslist1, [prod(size(cpslist1))/g.dim, g.dim]);
% maskall = scatter_binary_trajectory_nearest_neighbor(g.boundary.box, cpslist1);
% maskall = scatter_binary_trajectory_nearest_neighbor(g.boundary.box, cpslist);
maskall = scatter_multiple_label_trajectory_after_distance_transform(g, cpslist(:, :, :));
maskall = maskall > 0;
% maskall = mask_longtime_ex;
logalpha = get_log_weight_using_distance_transform_tablegaussian(maskall, g.h, g.sigma2);
alpha = exp(logalpha);
for ii = 1: length(clist)-1
ind_t1 = clist(ii);
ind_t2 = clist(ii+1);
% create velocity field using RBF decreasing function
vfield = get_stationary_vield_copy_paste_decreasing(g, xfield_0, cpslist(ind_t1:ind_t2, :, :), alpha);
if 0
% smoothing the velocity field in time by averaging the future velocity
% field, aiming to removing folding patten. The smoothing region is the
% non-critical region
% fixed value masks
mask_label = scatter_multiple_label_trajectory_after_distance_transform(g, cpslist(ind_t1:ind_t2, :, :));
el = strel('disk', g.h * 5);
mask_label_dilate = imdilate(mask_label, el);
% [gx, gy] = gradient(mask_label);
% mask_label_bounds = (gx.*gx + gy.*gy > 0);
mask_noncritical = (mask_label_dilate == 0);
% mask_noncritical = mask_noncritical & (1- (mask_label > 0));
if ii < length(clist)-1
ind_t3 = clist(ii+2);
vfield_forward = get_stationary_vield_copy_paste_decreasing(g, xfield_0, cpslist(ind_t2:ind_t3, :, :), alpha);
else % smooth backwards
ind_t3 = clist_ex(min(find(clist_ex > clist(end) )));
vfield_forward = get_stationary_vield_copy_paste_decreasing(g, xfield_0, cpslist_ex(ind_t2:ind_t3, :, :), alpha);
end;
q=10;
figure(ii+2000); clf;
quiver(X(1:q:end,1:q:end), ...
Y(1:q:end,1:q:end), ...
vfield_forward(1:q:end,1:q:end, 1) , ...
vfield_forward(1:q:end,1:q:end, 2) , 1);
hold on;
for kk = 1:nb_cps;
plot(cpslist_ex(ind_t2:ind_t3, 1, kk), cpslist_ex(ind_t2:ind_t3, 2, kk), 'r.');
end;
hold off;
%
axis image;
vfield_1 = vfield(:, :, 1);
vfield_2 = vfield(:, :, 2);
vfield_forward_1 = vfield_forward(:, :, 1);
vfield_forward_2 = vfield_forward(:, :, 2);
tmpw = 1;
vfield_1(mask_noncritical) = tmpw * vfield_1(mask_noncritical) + (1-tmpw) * vfield_forward_1(mask_noncritical);
vfield_2(mask_noncritical) = tmpw * vfield_2(mask_noncritical) + (1-tmpw) * vfield_forward_2(mask_noncritical);
vfield(:, :, 1) = vfield_1;
vfield(:, :, 2) = vfield_2;
end;
% vfield = smooth_field(vfield, 1, 'Gaussian');
% another way to create vector field:
% fix the values inside the mask as the accurate values
% and use smoothing / interpolation for the rest of the field
% mask_label = scatter_multiple_label_trajectory_after_distance_transform(g, cpslist(ind_t1:ind_t2, :, :));
% vfield_inside_mask_accurate = get_stationary_vfield_from_labeled_mask(g, xfield_0, mask_label);
% vfield = smooth_field(vfield_inside_mask_accurate, 20, 'PrecondtionVariationalWithBoundary', mask_label, vfield);
% vfield = get_stationary_vield_copy_paste(g, xfield_0, cpslist(ind_t1:ind_t2, :, :), tlist(ind_t1:ind_t2));
% [vfield_backbone, ind_backbone] = scatter_interploate_trajectory_nearest_neighbor([leftB, rightB, bottomB, topB], cpslist(ind_t1:ind_t2, :, :), vcpslist(ind_t1:ind_t2, :, :));
% vfield = smooth_field(vfield_backbone, g.vfield_smooth_sigma, 'PrecondtionVariational');
% replace v on trajectories with exame numbers
% vfield(ind_backbone) = vfield_backbone(ind_backbone);
% vfield = vfield_backbone;
q=10;
figure(ii+1000); clf;
% quiver(X(1:q:end,1:q:end), ...
% Y(1:q:end,1:q:end), ...
% vfield(1:q:end,1:q:end, 1) / max(vfield(:)) * 2, ...
% vfield(1:q:end,1:q:end, 2) / max(vfield(:)) * 2, 0);
quiver(X(1:q:end,1:q:end), ...
Y(1:q:end,1:q:end), ...
vfield(1:q:end,1:q:end, 1) , ...
vfield(1:q:end,1:q:end, 2) , 1);
hold on;
for kk = 1:nb_cps;
plot(cpslist(ind_t1:ind_t2, 1, kk), cpslist(ind_t1:ind_t2, 2, kk), 'r.');
% quiver(cpslist(ind_t1:ind_t2, 1, kk), cpslist(ind_t1:ind_t2, 2, kk), vcpslist(ind_t1:ind_t2, 1 ,kk) * 0.02, vcpslist(ind_t1:ind_t2, 2 ,kk) * 0.02, 1, 'r');
end;
hold off;
%
axis image;
yfield_delta = exp_mapping(vfield, X, Y, tlist(ind_t2)-tlist(ind_t1), 10);
yfield_current = compose_phi(yfield_current, yfield_delta, X, Y);
for k = 1:nb_cps
idx_p = find(X==cps(1,k) & Y==cps(2,k));
y1 = yfield_current(:,:,1);
y2 = yfield_current(:,:,2);
cpspiecelist(ii+1, :, k) = [y1(idx_p), y2(idx_p)];
end;
end;
pad=0;
fil=5;
figure(109); clf;
% plot trajectory of control points (cps) using ode solution
hold on;
clrs='gbr';
markers='o*v';
for jj = 1:length(clist)
for ii = 1:nb_cps
% plot(squeeze(cpslist(:, 1, ii)), squeeze(cpslist(:, 2, ii)), ['-', clrs(mod(ii, length(clrs))+1), '*']);
plot(squeeze(cpslist(clist(jj), 1, ii)), squeeze(cpslist(clist(jj), 2, ii)), ...
[clrs(mod(ii, length(clrs))+1), markers(mod(jj, length(markers))+1)], 'MarkerSize', 10);
end;
end;
hold off;
% meshplot(X(pad*fil:fil:end-pad*fil, pad*fil:fil:end-pad*fil), Y(pad*fil:fil:end-pad*fil, pad*fil:fil:end-pad*fil), 'Color', 'g');
% meshplot(yfield_current(pad*fil:fil:end-pad*fil, pad*fil:fil:end-pad*fil, 1), yfield_current(pad*fil:fil:end-pad*fil, pad*fil:fil:end-pad*fil, 2), 'Color', 'b');
meshplot(X(pad*fil+1:fil:end-pad*fil, pad*fil+1:fil:end-pad*fil), Y(pad*fil+1:fil:end-pad*fil, pad*fil+1:fil:end-pad*fil), 'Color', 'g');
meshplot(yfield_current(pad*fil+1:fil:end-pad*fil, pad*fil+1:fil:end-pad*fil, 1), yfield_current(pad*fil+1:fil:end-pad*fil, pad*fil+1:fil:end-pad*fil, 2), 'Color', 'b');
% hold on;
% for jj = 1:nb_cps
% for ii = size(cpspiecelist, 1):size(cpspiecelist, 1)
% quiver(cpspiecelist(1,1,jj), ...
% cpspiecelist(1,2,jj), ...
% cpspiecelist(ii,1,jj)-cpspiecelist(1,1,jj), ...
% cpspiecelist(ii,2,jj)-cpspiecelist(1,2,jj), ...
% 1, clrs(mod(jj, length(clrs))+1), 'LineWidth', 1);
% end;
% end;
% hold off;
% plot desired position
% cps_desired_target = get_affine_on_cps(g);
% hold on;
% for jj = 1:nb_cps
% quiver(cps(1,jj), ...
% g.cps(2,jj), ...
% cps_desired_target(1,jj)-cps(1,jj), ...
% cps_desired_target(2,jj)-cps(2,jj), ...
% 0, 'c', 'LineWidth', 2);
% end;
% hold off;
axis equal;
%
% figure(3); clf;
% plot(clist, tlist(clist), 'b*');
% title('clist');