GeometricaPlus

Contents

Drawing

• Basic functions in 2 D and 3 D | Animation | Origin of lines and planes | Range of variations of the parameters | Arrow | Legend | Painting | Canonical view point | Control of display

Points

• Cartesian point | Parametric point | Bound point
• Barycenter | Brianchon point | Center | Center of curvature, of gravity and of perspective | Circumcenter | Excenters | Fermat point | Foci | Incenter | Line and plane origin | Orthocenter | Pole | Vertices

Lines and Planes

• Cartesian line and plane | Pencil | Euclidean line and plane | Conjugate line | Conjugate plane | Parallel | Normal plane | Tangent
• Altitudes | Asymptotes | Axes | Axis of perspective | Bisector | Diagonals | Directrices | Euler's line | Generators | Imaginary, infinity and indeterminate line | Imaginary, infinity and indeterminate plane | Medians | Normals | Pascal line | Polar | Symmetry planes

Conics

• Cartesian conic in 2 D and 3 D | Pencil | Euclidean conic | Conic elements | Normal conic
• Imaginary and real circle | Circumcircle | Euler's circle | Excircles | Incircle | Imaginary and real ellipse | Parabola | Hyperbola

Quadrics

• Cartesian quadric | Euclidean quadric | Quadric elements
• Sphere | Circumsphere | Edge sphere | Exspheres | Insphere | Ellipsoid | Quadric cone | Elliptic cylinder | Hyperbolic cylinder | Parabolic cylinder | Elliptic paraboloid | Hyperbolic paraboloid | Hyperboloid of one sheet | Hyperboloid of two sheets

Curves, surfaces and volumes

• General definitions | Parameter range | Libraries of curves and surfaces | Arc and strip | Evolute of a curve | Isolines of a surface | Axisymmetric and ruled surfaces | Cubic or Bezier fits | Transformation into regions | Wall and pipe
• Cardioid | Cassini's ovals | Cissoid | Conchoid | Cycloid | Hypotrochoid | Petal | Racetrack | Spiral | Trochoid General cone and cylinder | Helix | Helicoid | Helicoidal staircase | Möbius' strip | Torus | Viviani's window

Polygons and Polyhedra

• General definitions | Cartesian and generalized segments | Operations on segments | Elements of polygons and polyhedra | Orthogonal and parallel polygons | Special polygons and polyhedra | Graphics complex | Oriented segments : 2D and 3D Frenet systems

Transformations

• Affine | Homothety | Symmetries and inversion | Projection and inverse projection | Rotation | Translation | Shear | Embedding a 2 D object into 3 D | Creation of regions

Intersections

• 2 D intersections : Line, conic or polygonal line | Line and general curve | General curves using an interactive technique
• 3 D intersections : Coplanar lines or conics | Plane with line, plane, polygonal line, polyhedron, quadric, cone, cylinder, general curve or surface

Affine Notions

• Barycentric coordinates | Cartesian coordinates | Cross and section ratios | Sorting points on lines and conics

Metric Notions

• Angle of vectors, lines and planes | Distance between points, parallel lines and parallel planes | Length, curvature and torsion of curves | Radius of circles and spheres | Eccentricity of conics | Areas of closed curves and surfaces | Volume limited by a surface

Tests and Theorems

• Collinear points, segments, and straight lines | Coplanar points, segments, straight lines and planes
• Congruent and similar triangles | Regular polygon | Platonic solid
• Point on line, conic, polygonal line, plane, or quadric | Line on plane or quadric | Segment on line, plane, or quadric | Conic on plane or quadric
• Type of special surfaces and polyhedra
• Line, polygonal line or conic tangent to a conic | Plane or line tangent to a quadric. Identical objects
• Theorems : Brianchon | Desargues | Euler | Pappus | Pascal | Thales | Villarceaux