Graph

An object in CalcMe is plotted in Graph; but Graph is much more than a simpler viewer, we can build segments, vectors, lines, and conic sections. Moreover, the handwritten geometry recognition allows us to draw by hand, as we do on paper, and it will translate our drawings to mathematical objects.

We can draw points as we would do on a sheet. Select the Point tool, move the mouse to the desired position and left-click. A new point will be created where we place the mouse cursor. Notice that if the cursor is close to an integer point, the magnetic grid attracts the mouse to it.

Moreover, if there is already a graph and the mouse is close to remarkable positions, the new point will be created in such a position. The same happens when the mouse is close to the axis. We can think about it as a magnet to important points.

Given two points, we can construct either a line, a segment, a ray or a vector.

More than two points define a parallelogram, a polyline or a polygon. Notice that you can see the parallelogram's area while you are creating it. That's also possible when the parallelogram or the polygon are finished if the cursor is inside them.

Given three points, we can draw an arc. Select the Arc tool, create three different points and an arc passing through such three points will appear.

Circumferences can be drawn in two different ways. Either we choose the center and its radius, or we choose three points so that a circumference passing through them is constructed.

To write a parabola, we choose its directrix, and then we move the mouse to place the focus.

Ellipses are constructed given their focus and its eccentricity.

For hyperbolas a similar manner is used: we choose the focus and then the eccentricity.

In a more general approach, we can locate five points, and a conic passing through them will be constructed. The conic will change as we move the fifth point.

Given a configuration of objects in the CalcMe graph, it's possible to get the area of the closed regions that they define.

Moreover, given two objects, it's possible to get the angle counterclockwise between them.

Finally, given an object, it's possible to get its length (if the object is bounded) or the length of a particular section. By the way, given two different objects, it's also possible to get the distance between them.

Given any object drawn in Graph, you can modify the color, width, and style of its graphic representation.

Furthermore, we can add text next to the plotted objects to add information that the default label doesn't include. The text format can be configured as in the sheet.

Apart from building an object following a specific format, we can directly draw by hand, as we would do on a paper, over the graphing area and our drawing will be converted to a mathematical object.

Currently, our drawings will be converted to one of the following objects:

• Points
• Segments
• Polysegments
• Polygons
• Ellipse arcs
• Ellipses
• Circle arcs
• Circles
• Parabolas
• Sinusoids

Points

Just click on the grid, and a point will be built or draw a small circle. If we are close to the axis, the point is snapped to it.

Segments

Left-click with the mouse and drag through the screen. Release the button, and a segment will be created.

Polysegments and polygons

Draw concatenated segments so a polysegment or a polygon (if you close it) is built.

Interaction between objects

If we draw a segment and then draw a perpendicular segment to the first one, it will create an orthogonal line perpendicular to the former segment. If we move the original segment, the line automatically moves, so it keeps being orthogonal.

Similarly, if we draw a segment and then draw a parallel segment to the first one, a parallel line will be created. If we move the original segment, the line automatically moves, so it keeps being parallel.

Arcs

Draw a portion of an ellipse or circumference and an arc will be constructed.

Circles and ellipses

Draw a circle or an ellipse as you would do in longhand.

Parabolas

Similarly, draw a parabola (vertical or sideway) and it will converted to a graph object.

Sinusoidal

We can also draw sinusoidal functions.