  Dictionary of Geometry Home ▸ The dictionaries ▸ Dictionary of Geometry  Geometry suite Transformations Constructions Triangles Drawings
 Geometry suite This suite defines the requested properties for geometric objects. A geometric object here is actually an AppleScript's record.

point n

transformation n : a list of 6 real numbers {a, b, c, d, tx, ty}. Any point will undergo the mapping: {x, y} -> {ax + cy + tx, bx + dy + ty}. The Identity transformation is {1, 0, 0, 1, 0, 0}

straight line n

properties

point list of real : coordinates of the origin

angle real : the orientation in radians

limits list of real : optional field {xmin,xmax}. If the field is present, geompath draws the line from abscissa xmin thru abscissa xmax; abscissa 0 is "point"

line segment n

properties

point list of real : coordinates of the origin

endpoint point : coordinates of the endpoint

limits list of real : optional field {xmin,xmax}. If the field is present, geompath draws the line segment from abscissa xmin thru abscissa xmax; abscissa 0 is "point" and abscissa 1 is "endpoint"

circle n : a circle

properties

point list of real : coordinates of the center

limits list of real : optional field {amin,amax}. If the field is present, geompath draws an arc from angle amin to amax, counter-clockwise; angle 0 corresponds to horizontal axis

ellipse n : an ellipse. To create an ellipse, use "create ellipse" to create an ellipse or apply a transformation to a circle

properties

point list of real : coordinates of the center

transformation list of real : a 2 by 2 matrix m. m is symmetric and has determinant 1. The ellipse is the image of a circle of radius "radius" thru the transformation defined by m and the center

limits list of real : optional field (see circle)

 Transformations

apply v : apply a transformation to a geometric object or to a transformation

apply transformation

to any : a geometric object, a point or a transformation

→ record : or transformation

symmetry v : create (or apply) a symmetry

symmetry [record] : a point, a straight line, a circle..., or list

about any : point or straight line

→ any : a transformation if the direct parameter is missing, else the transformed direct parameter

rotate v : create (or apply) a rotation

rotate [record] : a point, a straight line, a circle..., or list

[thru real] : angle in radians

[about point] : the fixed point (default {0,0})

→ any : a transformation if the direct parameter is missing, else the transformed direct parameter

homothecy v : create (or apply) a homothecy

homothecy [record] : a point, a straight line, a circle..., or list

ratio real : similitude ratio

[about point] : the fixed point (default {0,0})

→ any : a transformation if the direct parameter is missing, else the transformed direct parameter

similarity v : create (or apply) a similarity

similarity [record] : a point, a straight line, a circle..., or list

[thru real] : angle in radians

ratio real : similitude ratio

[about point] : the fixed point (default {0,0})

→ any : a transformation if the direct parameter is missing, else the transformed direct parameter

translate v : create (or apply) a translation

translate [record] : a point, a straight line, a circle..., or list

thru point : translation vector

→ any : a transformation if the direct parameter is missing, else the transformed direct parameter

inverse transformation of v : create the inverse transformation

inverse transformation of transformation

 Constructions

line from v : create a straight line (an AppleScript's record) from a pair of points

line from list of point : 2 points or a line segment

create point on v

create point on straight line : or line segment or circle

at real : the abscissa of the point on the line (in the line segment units if the direct parameter is a line segment) or the angle of the vector from the center to the desired point if the direct parameter is a circle

create ellipse v

create ellipse point : center of the ellipse

tilt real : the angle between the global x-axis and the ellipse's xaxis

bisector v

bisector list of point : 3 points. {A, O, A'} to get the bisector thru O of the angle AOA'

straight line : the bisector with O as point property

perpendicular bisector v

perpendicular bisector list of point : 2 points or a line segment

straight line : perpendicular bisector with middle of direct parameter as point property

perpendicular to v

perpendicular to straight line

thru point

parallel to v

parallel to straight line

thru point

project v

project point

onto straight line

[along straight line] : or an angle in radians

intersect v

intersect list of record : a list of 2 objects: straight lines, circles or ellipses

→ list of point : or empty list

distance from v

distance from any : geometric object

to any : another geometric object

→ real

nearby points from v

nearby points from any : geometric object

to any : another geometric object

→ list of point : a list of two points. The first one belongs to the direct parameter and the second one to the "to" parameter

barycenter v : compute the barycenter of a list of points

barycenter list of point : a point may be a list of 2 real number or a record with a point property

[weight list of real] : the list of the weigths. Same size than the list of points

point : the barycenter

 Triangles

orthocenter v : orthocenter of 3 points

orthocenter list of point : a list of 3 points

point : the orthocenter

incenter v : incenter of 3 points

incenter list of point : a list of 3 points

circle : the incenter

circumcenter v : circumcenter of 3 points

circumcenter list of point : a list of 3 points

circle : the circumcenter

 Drawings

geompath v : draw a geometric object. If the object has a property "limits" (as a list of 2 real numbers), geompath will use it

geompath record : a straight line, a line segment or a circle.

markpoint v : mark a point with a small tick

markpoint point : or a real: the abscissa of the point on the line

on straight line : or a line segment

magnitude real : length of the tick in pixels

markrightangle v : mark a right angle with a square

markrightangle list of point : a list of 3 points defining the right angle

magnitude real : size of the square in pixels

markangle v : mark an angle with small arcs

markangle list of point : a list of 3 points defining the angle to mark

magnitude real : size of the smallest radius in pixels

[narcs integer] : number of arcs. Default 1