Geometry Applet Programming Reference

version 2.2

*** If you can read this, you're only seeing an image, not the real java applet! ***

The Geometry Applet was provided to Science Buddies by kind permission of its author, Professor David Joyce. The applet was written to illustrate Euclid's Elements. Above you see an icosahedron, that is, a regular 20-sided solid, constructed according to Euclid's construction in proposition XIII.16.

Another example using this Geometry Applet illustrates the Euler line of a triangle.

Here's how you can manipulate the figure that appears above. If you click on a point in the figure, you can usually move it in some way. A free point *, usually colored red, can be freely dragged about, and as they move, the rest of the diagram (except the other free points) will adjust appropriately. A sliding point *, usually colored orange, can be dragged about like the free points, except their motion is limited to a straight line, a circle, a plane, or a sphere, depending on the point. Other points can be dragged to translate the entire diagram. If a pivot point * appears, usually colored green, then the diagram will be rotated and scaled around that pivot point.

Try dragging around some of the points in the diagram above.

Also, if you type r or the space key while the cursor is over the diagram, then the diagram will be reset to its original configuration. If you type u or return the figure will be lifted off the page into a separate window. Typing d or return while the cursor is over the original window will return the diagram to the page. Note that you can resize the floating window to make the diagram larger.

Parameters

Parameters are specified in the following format:

<param name=yyyy value="zzzz">

where the name, yyyy, may be one of the following:

background - the background color (for specifying the value, see below);
font - the font for displaying letters in the figure (default TimesRoman);
fontsize - the size of the font for displaying letters (default 18);
align - the alignment method for positioning letters (for specifying the value, see below);
title - the title of the figure, used for a floating frame;
debug - the debugging switch, by default, off;
pivot - the name of a pivot point, if any;
e[i] - an element. The elements are numbered from 1 on up (for specifying the value, see below).

Elements

The format for an element is a little complicated. Here is the minimal specification for an element:

<param name=e[1] value="A;point;free;50,50">

Each element has a number, which appears in the square brackets, "[ ]". The number for this element is 1, which means that it is the first element to be created. The "value" for each element consists of up to 8 arguments, separated by semicolons. The first four arguments are required:

a name,
an element class,
a construction method, and
construction data.

For the example element above, its name is "A". Its class is point. Its construction method is free, which means it can be freely dragged about. Its construction data is "50,50", which means that it will be initially placed at pixel coordinates (50,50). (Note that the parameters of the construction data are separated by commas, and that the semicolon following the final argument may be omitted.) The coordinate system follows the conventions of screen coordinates: the origin of the coordinate system is the top left corner of the diagram; the positive x-axis is to the right; the positive y-axis is down.

Colors

The four optional arguments (#'s 5–8) are used to specify colors for attributes of an element. If these arguments are omitted, then default colors are used. The optional arguments are (continuing the previous list):

the color of the name of the element;
the color of the 0-dimensional parts (points) of the element;
the color of the 1-dimensional parts (lines or arcs) of the element; and
the color of the 2-dimensional parts of the element (if any).

Colors can be declared in a three different ways.

A single word specifying the color may be given. These possible colors are * black, * blue, * cyan, * darkGray, * gray, * green, * lightGray, * magenta, * orange, * pink, * red, * white, and * yellow. If the word "random" is specified, then a randomly chosen pastel will be used. If an element is specified as "background", then it will be given the background color; if "brighter", then a brighter version of the background; if "darker", then a darker version of the background; and if "none" then it won't appear.
Specific colors may be given by their red, green, and blue components as six hexadecimal digits in an rrggbb format (i.e., the first pair of digits specifies the red component, the second pair of digits specifies the green component, and the third pair of digits specifies the blue component of the color). A value of "0"
A color can be given as a triple of decimal numbers separated by commas to indicate hue (0 to 360), saturation (0 to 100), and brightness (0 to 100).

Here is an example of an element with all eight arguments:

<param name=e[7] value="semiAC;sector;sector;ACm,A,C;0;0;blue;200,3,95"> For this example element, its name is "semiBA". Its class is sector. Its construction method is also sector. Its construction data is "ACm,A,C" (three previously-defined points). Its name will not appear on the diagram, nor will its points, because the next two arguments are both 0. Its outline will appear in blue. Finally, it will be filled with a light blue color, specified by the triple "200,3,95" (for hue, saturation, and brightness).

Alignment

Currently, there are five values for alignment: ABOVE, RIGHT, BELOW, LEFT, and CENTRAL (the default). For ABOVE alignment, the names of points appearing in the diagram will appear above points. Analogously for RIGHT, BELOW, and LEFT. For CENTRAL alignment, letters will appear away from the center of the diagram.

Element classes and construction methods

There are eight different element classes: point, line, circle, polygon, sector, plane, sphere, and polyhedron. Only the first five classes are used in plane geometry. All can be used in solid geometry.

Each class has several construction methods. The eight tables below briefly explain these construction methods.

Special notes

1. Any time two points are needed in a construction, one line may be given instead. For instance, if AB has already been defined as a line that connects points A and B, then the triangle ABC can be defined by either of these:

value="ABC;polygon;triangle;A,B,C" value="ABC;polygon;triangle;AB,C"

2. Those constructions that can only be used in solid geometry are indicated with a light green background color.

3. Optional data elements are indicated in the tables by square brackets. In particular, [z] indicates z is an optional integer, and [plane A] indicates A is an optional plane. The optional data elements are only used in solid geometry; they should always be omitted in plane geometry.

3a. When an optional third coordinate [z] is not specified, it is taken to be 0 so that the point lies in the xy-plane, that is, the plane of the screen.

3b. When an optional plane such as [plane A] is not specified, it is assumed to be the xy-plane.

4. Data parameters come in three kinds: (1) integers, (2) points, and (3) other elements. These are indicated in separate lines in the tables. As long as the parameters of each kind come in the right order, they will be interpreted properly. Parameters of different kinds may be listed as you like.

Index of tables

Table 1: Element class point: Constructions: free, midpoint, intersection, first, last, center, lineSlider, circleSlider, circumcenter, vertex, foot, cutoff, extend, parallelogram, similar, perpendicular, proportion, invert, meanProportional, planeSlider, sphereSlider, angleBisector, angleDivider, fixed, lineSegmentSlider
Table 2: Element class line: Constructions: connect, angleBisector, angleDivider, foot, chord, bichord, perpendicular, cutoff, extend, parallel, similar, proportion, meanProportional
Table 3: Element class circle: Constructions: radius, circumcircle, invert, intersection
Table 4: Element class polygon: Constructions: square, triangle, quadrilateral, pentagon, hexagon, equilateralTriangle, parallelogram, regularPolygon, starPolygon, similar, application, octagon, face
Table 5: Element class sector: Constructions: sector, arc
Table 6: Element class plane: Constructions: 3points, perpendicular, parallel, ambient
Table 7: Element class sphere: Construction: radius
Table 8: Element class polyhedron: Constructions: tetrahedron, parallelepiped, prism, pyramid

Element class point
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
free	integers x, y	a freely dragable point in the screen plane with initial coordinates (x,y,0)
midpoint	points A, B	the midpoint of a line AB
intersection	points A, B, C, D [plane E]	the intersection of two lines AB and CD in the plane E
intersection	points B, C plane A	the intersection of the plane A and the line BC
first	points A, B	the first end A of the line AB
last	points A, B	the last end B of the line AB
center	circle A	the center of the circle A
center	sphere A	the center of the sphere A
lineSlider	points A, B integers x, y,[z]	a point that slides along a line AB with initial coordinates (x,y,z)
circleSlider	circle A integers x, y,[z]	a point that slides along a circle A with given initial coordinates (x,y,z)
circumcenter	points A, B, C [plane D]	the center of a circle ABC passing through 3 points A, B, and C in the plane D
vertex	polygon A integer i	a vertex A_i of the polygon A₁A₂...A_n with index i
foot	points A, B, C	the foot of a perpendicular drawn from A to a line BC
foot	point A plane B	the foot of a perpendicular drawn from A to a plane B
cutoff	points A, B, C, D	the point E on a line AB so that AE = CD
extend	points A, B, C, D	the point E on a line AB so that BE = CD
parallelogram	points A, B, C	the 4th vertex D of a parallelogram ABCD given 3 vertices A, B, and C
similar	points A, B, D, E, F [planes C, G]	the point H so that triangle ABH in plane C is similar to triangle DEF in plane G
perpendicular	points A, B, [plane C]	the point D so that AD is equal and perpendicular to AB in plane C
	points A, B, D, E [plane C]	the point F so that AF is perpendicular to AB in plane C and equals DE
	points A, C, D plane B	the point E on the line perpendicular to plane B passing through A so that the distance from E to B equals CD
proportion	8 points A, B, C, D, E, F, G, H	the point I on GH so that AB:CD = EF:GI
invert	point A circle B	the image of a point A inverted in the circle B
meanProportional	6 points A, B, C, D, E, F	the point G on EF so that AB:CD = CD:EG
planeSlider	plane A integers x, y, z	a point that slides on the plane A with initial coordinates (x,y,z)
sphereSlider	sphere A integers x, y, z	a point that slides on the sphere A with initial coordinates (x,y,z)
angleBisector	points A, B, C [plane D]	The point at the intersection of the angle bisector of angle BAC and the line BC in plane D
angleDivider	points A, B, C [plane D] integer n	The point E on the line BC so that angle BAE is the n^th part of the angle BAC in plane D
fixed	integers x, y,[z]	the fixed point with coordinates (x, y, z)
lineSegmentSlider	points A, B integers x, y,[z]	a point that slides along within the line segment AB with initial coordinates (x,y,z)
harmonic	points B, C, D	the harmonic conjugate of B with respect to C and D

Element class line
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
connect	points A, B	the line AB connecting two points A and B
angleBisector	points A, B, C [plane D]	the line AE bisecting angle BAC with E on BC in plane D
angleDivider	points A, B, C [plane D] integer n	the line AE with E on BC so that BAE is the n^th part of the angle BAC in plane D
foot	3 points A, B, C	the line AD drawn perpendicular to BC in the screen plane
foot	point A plane B	the line AD drawn perpendicular to plane B with the point D lying on B
chord	points A, B circle C	the intersection of the line AB in the circle C
bichord	circles A, B	the common chord connecting the two intersection points of the circles A and B
perpendicular	points A, B [plane C]	the line AD equal and perpendicular to AB in plane C
	points A, B, D, E [plane C]	the line AF perpendicular to AB in plane C equal to DE
	point A, C, D plane B	the line EF perpendicular to plane B passing through A equal to CD with E lying on B
cutoff	points A, B, C, D	the line AE equal to CD along the line AB
extend	points A, B, C, D	the line BE equal to CD so that A, B, and C are collinear with B between A and C
parallel	points A, B, C	the line AD parallel and equal to BC
similar	points A, B, D, E, F [planes C, G]	the line AH so that triangle ABH in plane C is similar to triangle DEF in plane G
proportion	8 points A, B, C, D, E, F, G, H	the line GI along GH so that AB:CD = EF:GI
meanProportional	6 points A, B, C, D, E, F	the line EG along EF so that AB:CD = CD:EG

Element class circle
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
radius	points A, B [plane C]	the circle with center A and radius AB in the plane C
radius	points A, B, C [plane D]	the circle with center A and radius BC in the plane D
circumcircle	points A, B, C [plane D]	the circle passing through 3 points A, B, and C in the plane D
invert	circles A, B	the image of circle A inverted in circle B
intersection	spheres A, B	the intersection of spheres A and B

Element class polygon
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
square	points A, B [plane C]	the square on a side AB in plane C
triangle	points A, B, C	the triangle ABC given 3 vertices A, B, and C
quadrilateral	points A, B, C, D	the quadrilateral ABCD given 4 vertices A, B, C, and D
pentagon	points A, B, C, D, E	the pentagon given 5 vertices
hexagon	points A, B, C, D, E, F	the hexagon given 6 vertices
equilateralTriangle	points A, B [plane C]	the equilateral triangle on a side AB in plane C
parallelogram	points A, B, C	the parallelogram ABCD given A, B, and C
regularPolygon	points A, B integer n	the regular polygon on a side AB given the number of vertices n
starPolygon	points A, B integers n, d	the star polygon on a side AB given the number of vertices n and the density d
similar	points A, B, D, E, F [planes C, G]	the triangle ABH in plane C is similar to triangle DEF in plane G
application	polygon A points B, C, D	the parallelogram equal to the given polygon A with one side BC and one angle BCD
octagon	8 points A, B, C, D, E, F, G, H	the octagon given 8 vertices
face	polyhedron A integer n	the n^th face of polyhedron A

Element class sector
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
sector	points A, B, C [plane D]	the sector of a circle in plane D given the center A and two points B and C on the circumference
arc	points A, B, C [plane D]	the sector of a circle in plane D whose arc passes through the three points A, B and C

Element class plane
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
3points	points A, B, C	the plane passing through points A, B, and C
perpendicular	points A, B	the plane passing through point A and perpendicular to line AB
parallel	plane A point B	the plane passing through point A and parallel to plane B
ambient	point A	the ambient plane of point A
ambient	circle A	the ambient plane of circle A

Element class sphere
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
radius	points A, B	the sphere with center A and radius AB
radius	points A, B, C	the sphere with center A and radius BC

Element class polyhedron
(argument #2)

Construction method (argument #3)	Construction data (argument #4)	Description
tetrahedron	points A, B, C, D	the tetrahedron given four vertices
parallelepiped	points A, B, C, D	the parallelepiped with three edges AB, AC, and AD
prism	polygon A points B, C	the prism with base A and side edges parallel and equal to BC
pyramid	polygon A point B	the pyramid with base A and apex B

Source files

The Geometry Applet uses a Slate Canvas put all the Elements on. The slate can be lifted off into a separate window, and that uses ClientFrame, a subclass of Frame. An Element is a generic thing which is subclassed in eight different ways to give actual elements that can be displayed. These eight classes are further subclassed, too.

PointElement with subclasses AngleDivider, CircleSlider, FixedPoint, Foot, Harmonic, Intersection, IntersectionPL, InvertPoint, Layoff, LineSlider, MeanProportional, Midpoint, PlaneFoot, PlaneSlider, Proportion, Similar, and SphereSlider.
LineElement with subclasses Bichord, Chord, Perpendicular, and PlanePerpendicular.
CircleElement with subclasses Circumcircle, IntersectionSS, and InvertCircle.
PolygonElement with subclasses Application, and RegularPolygon.
SectorElement with subclass Arc.
PlaneElement with subclasses ParallelP and PerpendicularPL,
SphereElement.
PolyhedronElement with subclasses Prism and Pyramid.
The source files *.java are zipped in the file CompSci_GeometryAppletSource.zip. The class files *.class are zipped, but uncompressed, in the file Math_GeometryApplet.zip.

Geometry Applet Programming Reference

Related Links

version 2.2

Parameters

Elements

Colors

Alignment

Element classes and construction methods

Special notes

Index of tables

Element class point(argument #2)

Element class line(argument #2)

Element class circle(argument #2)

Element class polygon(argument #2)

Element class sector(argument #2)

Element class plane(argument #2)

Element class sphere(argument #2)

Element class polyhedron(argument #2)