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The plus of Cabri II Plus
Dropdown menus, a more user-friendly interface
Simply by right-clicking on an object with the mouse a contextual menu is displayed for rapid choice of an attribute. It shows the type of object, as well as the list of objects used in its construction. The information shown by the cursor during construction is clearer. The left-hand figure shows the contextual dropdown menu of an intersection between a triangle and a straight line. The triangle is thus highlighted (selected in the menu) You can choose a line color, a text color or a fill-in color using the 'Variable Color' or 'Variable Fill Color' attributes. Using the menu you can also change the opacity of objects, noting that opaque objects cannot mix colors with intersecting inferior surfaces.
Improved resolution of ambiguities
When clicking on a location with several superimposed images, a dropdown menu is shown to aid with selection. By running through this menu the various objects associated with the particular construction are highlighted. The right-hand example shows the menu displayed when you point the cursor at the point of intersection between the three bisectors of a triangle.
More attributes
Click on 'Options' and 'Show Attributes', the attributes menu offers even more possibilities. It lets you choose the color of a line, of text, fill-ins, and all the other attributes of an object, including the 'intelligent display' of lines.
Colors
Palette
Cabri II Plus has an extended palette of 36 separate colors and three shades of gray.
Mixtures
The ‘fill-in’ colors mix on-screen depending on the figure and the color synthesis. The example shows a mixture of the three primary colors, cyan, magenta and yellow, giving red, green, blue & black.
Customized
Color can be applied to all objects, lines and surfaces using a customized color by giving, on the worksheet, the intensity value for each component: Red, green and blue. This coloration procedure can be used during optical simulations to represent the various wavelengths of light. It can also be used in the study of scalar or vectorial fields. In the example below, the color corresponds to the values of a scalar field (polynomial in x & y), which applies color to a small disk with an active trace.
Attributes - Fonts and styles
The choice of font, style, size and attributes has been widened. Object names, numbers and equations can be inserted into a text zone and will be automatically updated when the figure is modified.With Cabri Geometry II Plus, every single object can be named.
Images insertion
Images can be attached to points, segment and convex quadrilaterals. Images can be files in the BMP, GIF or JPG format. They can be attached using the object dropdown menu (right-click mouse). The first example shown below shows a planet and its satellite in an elliptical orbit.
The second shows an image of a piston rod attached to a segment of a figure. The whole assembly may be animated to show the moving parts of an engine.
Expressions
Cabri II Plus offers a new type of object: the Expression. The Expression tool allows you to enter in the text form a mathematical expression containing variables (all operators from the calculator can be used). For example, '3*x-2*y+1' is an expression containing variables 'x' and 'y'. The 'Apply an Expression' tool allows you to evaluate the result of an expression by indicating which values on the drawing sheet are to be used for replacement of the variables in the expression. Moreover, if an expression is defined in function of 'x', this tool allows you to graph y=f(x) designating the system of axes of your choice. The opposite example illustrates this possibility with expression 'x^3/5-x^2-x+4'. Expressions have many more applications, like the exploration of scalar or vector fields, defined on the plane, and associated to the locus of a point located on a coordinate system.
Smart lines
Cabri II Plus gives the user the possibility of showing just the significant sections of lines. Lines are intrinsically infinite in length, however, often only a small portion of each line is required to make the figure comprehensible. The rest adds nothing to its understanding. Using the ‘Smart Lines’ option they are thus cut just after the last point on each line in both directions. If you wish, you can add an arrow to each end. The example shows a Simson line for a triangle.
Loci
An intersection with a locus
Cabri II Plus is also capable of representing intersections with loci. The example shows a cardioid, the locus of point p with m varying around the circle.We can thus build the intersections of the curve with a small circle, centered about p, and thus obtain a good estimate of the tangent and normal of the curve p.
Displaying loci
Loci are displayed using a new, adaptive monitoring, algorithm, which returns the optimal resolution for display and printing with no further operator intervention.
A locus from a point on a mark
A construction involving a point on a grid or axe can be used to generate a locus. This locus is the set of points around the target object with the moving point tracing around all points on the grid. Such a locus can be used to explore scalar or vectorial fields.In the following example a point on a grid is associated with a circle, the radius of which is proportional to the value of a polynomial P in x & y. Then the locus of these circles is built and we obtain a visualization of the scalar field corresponding to the polynomial, thus an idea of the shape of the curve P(x,y)=0.
Algebraic Equation Curves
Digital methods as algebraic curves of up to and including degree 6. If the equation of a locus is considered to exceed this functional range, the equation cannot be determined. The calculations are carried out to the precision of the machine itself (64 bits), thus numerical errors may appear.The following example shows the equation of an asteroid in a circle.
