Detailed method of constructing textured cones with geometric sketchpad

1. Construct an ellipse. Construct horizontal ray AB, click and hold the custom tool icon, select [Ellipse (Center Vertex)] in [Conic Section A], and click two points C and D on ray AB to construct an ellipse.

2. Construct points and line segments. Construct two points E and J arbitrarily on the ellipse. Select point C to construct the perpendicular line of ray AB passing through point C, use the point tool to construct point G on the perpendicular line, and construct line segment GJ. Select points J, C, and E in sequence, [Measurement—[Angle].

3. Set color parameters. Select the line segment GJ and angle measurement value, [Display] - [Color] - [Parameter] - [Grayscale], select 0 to 120 for [Parameter Range], and check [Bidirectional Cycle]. (These two values ​​determine how big the angle starts and ends, and the color of the line changes in a two-way cycle from black to white)

4. Draw the cone trajectory. Select line segment GJ and point J, [Construction] - [Trajectory] to obtain the three-dimensional graphic cone. Right-click the track, [Properties]-[Drawing]-[Number of Samples] and change it to 1500 or a larger number. (Not too large)

5. Set the color. Select [Edit] - [Preferences] - [Color] to change the background color of the drawing area of ​​the artboard to make the graphics more layered.

6. Hide various unnecessary objects and complete.

Tip: Changing the position of point B1 can adjust the ellipse of the cone base. Changing the positions of points D and G can change the size of the cone. Changing the position of point E can fine-tune the direction of the conic projection light.

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