How to 3D plot a parametric curve WITH orthographic projections? - matlab

Question

How to generate a 3D plot of a parametric curve with the orthographic projections on the inside walls of the 3D plot, as shown in this video?
I can generate a 3D plot of the curve using the plot3 function but I am lost how to create the blue orthographic projections on the inner walls of the cube ...and the red dashed lines.
P.S.
Also, how to generate the 3 separate "Coordinate Functions" plots (not shown on the diagram above but shown in the video) ...and how to synchronize them together during the animation?

Answer 1

Well, this took a lot of time to write.
clear;clc;close all
t = 0:0.01:6;
x = cos(5*t);
y = sin(5*t);
z = t;
%for x,y,z as as general function of t
xmin = min(x);
xmax = max(x);
ymin = min(y);
ymax = max(y);
zmin = min(z);
zmax = max(z);
orangeColorRGB = [0.8500 0.3250 0.0980];
%3D plot
plot3DSubplot = subplot(3,2,[1 3 5]);
view(3)
grid on
title('Parametric curve in R^3')
xlabel('x(t)')
ylabel('y(t)')
zlabel('z(t)')
xyProjectionOffset = -0.5;
xzProjectionOffset = 1.5;
yzProjectionOffset = 1.5;
xlim([xmin max(xmax, yzProjectionOffset)])
ylim([ymin max(ymax, xzProjectionOffset)])
zlim([min(zmin ,xyProjectionOffset) zmax])
curve3D_marker = animatedline(plot3DSubplot,x(1),y(1),z(1),'Marker','o','Color','magenta'); %marker in 3D
curve3D = animatedline(plot3DSubplot, x(1),y(1),z(1),'Color','magenta','LineStyle','-','LineWidth',2); %3D curve
curve3D_projectedToXY = animatedline(plot3DSubplot,x(1),y(1),xyProjectionOffset,'Color','blue','LineStyle','-','LineWidth',2); %projection on xy
curve3D_projectionStraightLineToXY = animatedline(plot3DSubplot,x(1),y(1),z(1),'Color',orangeColorRGB,'LineStyle','--','LineWidth',2); %projection on xy
curve3D_projectedToXZ = animatedline(plot3DSubplot,x(1),xzProjectionOffset,z(1),'Color','blue','LineStyle','-','LineWidth',2); %projection on xz
curve3D_projectionStraightLineToXZ = animatedline(plot3DSubplot,x(1),y(1),z(1),'Color',orangeColorRGB,'LineStyle','--','LineWidth',2); %projection on xy
curve3D_projectedToYZ = animatedline(plot3DSubplot,yzProjectionOffset,y(1),z(1),'Color','blue','LineStyle','-','LineWidth',2); %projection on yz
curve3D_projectionStraightLineToYZ = animatedline(plot3DSubplot,x(1),y(1),z(1),'Color',orangeColorRGB,'LineStyle','--','LineWidth',2); %projection on xy
%x plot
xPlot = subplot(3,2,2);
grid on
title('Coordinates')
ylabel('cos(5t)')
xlim([t(1) t(end)])
ylim([xmin xmax])
xCoordinate = animatedline(xPlot,t(1),x(1),'Color','blue');
xCoordinate_projectedValue = animatedline(xPlot,t(1),x(1),'Color',orangeColorRGB,'LineStyle','--');
xCoordinateMarker = animatedline(xPlot,t(1),x(1),'Color','blue','Marker','o');
%y plot
yPlot = subplot(3,2,4);
grid on
ylabel('sin(5t)')
xlim([t(1) t(end)])
ylim([ymin ymax])
yCoordinate = animatedline(yPlot,t(1),y(1),'Color','blue');
yCoordinate_projectedValue = animatedline(yPlot,t(1),y(1),'Color',orangeColorRGB,'LineStyle','--');
yCoordinateMarker = animatedline(yPlot,t(1),y(1),'Color','blue','Marker','o');
%z plot
zPlot = subplot(3,2,6);
grid on
ylabel('t')
xlim([t(1) t(end)])
ylim([zmin zmax])
zCoordinate = animatedline(zPlot,t(1),z(1),'Color','blue');
zCoordinate_projectedValue = animatedline(zPlot,t(1),z(1),'Color',orangeColorRGB,'LineStyle','--');
zCoordinateMarker = animatedline(zPlot,t(1),z(1),'Color','blue','Marker','o');
for i=2:length(t)
% 3D plot & projections
addpoints(curve3D,x(i),y(i),z(i))
clearpoints(curve3D_marker)
addpoints(curve3D_marker,x(i),y(i),z(i))
%XY projection
addpoints(curve3D_projectedToXY,x(i),y(i),xyProjectionOffset)
clearpoints(curve3D_projectionStraightLineToXY)
addpoints(curve3D_projectionStraightLineToXY,[x(i) x(i)],[y(i) y(i)],[xyProjectionOffset z(i)])
%XZ projection
addpoints(curve3D_projectedToXZ,x(i),xzProjectionOffset,z(i))
clearpoints(curve3D_projectionStraightLineToXZ)
addpoints(curve3D_projectionStraightLineToXZ,[x(i) x(i)],[xzProjectionOffset y(i)],[z(i) z(i)])
%YZ projection
addpoints(curve3D_projectedToYZ,1.5,y(i),z(i))
clearpoints(curve3D_projectionStraightLineToYZ)
addpoints(curve3D_projectionStraightLineToYZ,[yzProjectionOffset x(i)],[y(i) y(i)],[z(i) z(i)])
%2D x plot
addpoints(xCoordinate,t(i),x(i))
clearpoints(xCoordinate_projectedValue)
addpoints(xCoordinate_projectedValue,[t(1) t(i)],[x(i) x(i)])
clearpoints(xCoordinateMarker)
addpoints(xCoordinateMarker,t(i),x(i))
%2D y plot
addpoints(yCoordinate,t(i),y(i))
clearpoints(yCoordinate_projectedValue)
addpoints(yCoordinate_projectedValue,[t(1) t(i)],[y(i) y(i)])
clearpoints(yCoordinateMarker)
addpoints(yCoordinateMarker,t(i),y(i))
%2D z plot
addpoints(zCoordinate,t(i),z(i))
clearpoints(zCoordinate_projectedValue)
addpoints(zCoordinate_projectedValue,[t(1) t(i)],[z(i) z(i)])
clearpoints(zCoordinateMarker)
addpoints(zCoordinateMarker,t(i),z(i))
drawnow
end
Outside the for-loop:
Define your subplots.
Define your lines in a somewhat object-oriented approach. Define lines with animatedline
including their
properties
(color, linewidth etc).
Define lines with animatedline with the intention to use only the marker.
Inside the for-loop:
Add the new points to those lines using addpoints.
Regarding the projections to the xy,yz,xz planes:
The projection of a point (x0,y0,z0) to the xy plane defined by z = -2 is (x0,y0,-2). Therefore when you have a point (x,y,z) you project to the correct plane in the same way.
For the vertical lines that connect the current point to the projection, at every update to the plot remove previous points and redraw them. That's why I first call
clearpoints
to remove any previous points and then addpoints to add 2 points for a straight line from the projection to the actual (x,y,z) point.
For the "marker-lines", again clearpoints and then add the new point.
After adding the points to all the lines, call
drawnow
before the next loop iteration for all lines to be updated at the same time (and for the updates to appear synchronized).