Instructions
Here are the instructions for my convex hull
applet.
Display canvas
Dragging with the left mouse button lets you look at the hull from
different directions. If you release the mouse button while dragging
the hull will start spinning. You can stop it spinning by clicking on
it. Dragging with the middle mouse button
(or holding down Meta and dragging) lets you slide the image around,
while dragging with the right mouse button (or holding down Alt and
dragging) lets you zoom in or out.
The triangle colours have the following meanings:
 Red: A triangle that has just been created.
 Yellow: A triangle that is about to be deleted.
 Blue: The back of any triangle.
 Cyan and Magenta: Triangles that belong to the left and right
subhulls in the Divide and Conquer algorithm.
 Cyan: Triangle selected in Quickhull algorithm.
 Green: Any other triangle.
The checkboxes that appear when you click twice on "More Controls" can be used to make triangles of any particular colour transparent.
Main Menu
Dimension Choice
 2D
 Show algorithms for twodimensional convex hull.
 3D
 Show algorithms for threedimensional convex hull.
Algorithm Choice
 Incremental
 Add points to hull one at a time updating the hull as we go.
 Gift Wrap
 Construct hull one edge (or face) at a time, moving from one edge
to an adjacent one.
 Divide and Conquer
 Divide the points into two equal sized subsets, recursively hull
each subset and then merge them together.
 QuickHull
 A variation on he incremental algoritm where each point is
associated with a face that it can see.
Point Distribution Choice
For a 3D hull, you have the following choices for the distribution of the points:
 In Sphere
 The points are chosen uniformly from inside a sphere.
 On Sphere
 The points are chosen uniformly from the surface of a sphere.
Note that all the points will be vertices of the convex hull.
 In Cube
 The points are chosen uniformly from inside a cube.
 On Paraboloid
 The points are chosen on the paraboloid z=x^{2}+y^{2}. This
distribution is interesting because the projection of the lower part
of the convex hull onto the XY plane is the Delaunay triangulation.
 Gaussian
 The points are chosen from a threedimensional Gaussian distribution.
 Wedge Block
 This is a particular configuration of points from Computational
Geometry in C that can cause the divide and conquer algorithm some
problems. It has exactly 16 points  unlike the other choices you
cannot set a different number of points.
For a 2D hull, you have the following choices for the distribution of the points:
In Circle
The points are chosen uniformly from inside a circle.
On Circle
The points are chosen uniformly from the boundary of a circle.
Note that all the points will be vertices of the convex hull.
In Square
The points are chosen uniformly from inside a square.
Points field
This lets you select the number of points to hull.
More Controls button
This lets you display more controls. The first time you click on the
button the Animation control menu is displayed,
the second time you click on the
button the Show menu is displayed, and
the third time you click on the
button the View menu is displayed.
To
display this menu you must click on the More Controls button.

 Start the animation of the currently selected convex hull algorithm.

 Stop the animation of the currently selected convex hull algorithm.

 Display the next frame of the animation.

 Display the previous frame of the animation.

 Display the first frame of the animation.

 Display the last frame of the animation

 You can enter the number of the frame that you want to see here.

 This lets you control the speed of the animation. Two clicks on
the right arrow doubles the speed; two clicks on the left arrow halves
it.

 Lets you hide the extra controls revealed by the More Controls button.
The checkboxes lets you control the visibility of objects. If the
check box is checked you can see the specified objects. To
display this menu you must click twice on the More Controls button.

 Triangles that do not belong to any other category.

 Triangles that have been added in the currect frame.

 Triangles that will be deleted in the next frame.

 The X,Y and Z axes

 The points that we are hulling. These are displayed in a layer in
front of the hull so that you can see the points inside the hull. If
you select 3D algorithms this box is unchecked so that points are
invisible. If
you select 2D algorithms this box is checked so that points are
visible.

 Triangles that are part of the left subhull in the divide and
conquer algorithm.

 Triangles that are part of the right subhull in the divide and
conquer algorithm.

 The triangle selected in the QuickHull algorithm.
View Menu
These buttons let you control the viewing direction for 3D hulls. To
display this menu you must click three times on the More Controls button.

 This lets you choose between a perspective projection (objects that are
further away are drawn smaller) and an orthographic projection (objects are
drawn the same size, no matter how far away they are).

 The view direction is looking up the z axis. With this view
direction and points chosen "On Paraboloid", you are looking at an
animation of a Delaunay triangulation algorithm.

 The view direction is looking down the z axis. This view is
chosen automatically when you select a "2D" from the dimension choice.

 The view direction is looking up the y axis.

 The view direction is looking up the y axis.

 The view direction is looking up the x axis.

 The view direction is looking down the x axis.

 Go to the home view. This is the starting view, or the view
direction set by the "Set Home" button.

 Set the home view to be the current view. You can return to this
view by pressing the "Home" button.
lambert@cse.unsw.edu.au
Last modified: Fri Sep 25 14:37:59 AET 1998