### Bezier Curves

Graphs one segment of a Bezier curve using endpoints and control points.
How to use   ||   Examples   ||   Other Notes

How to use
• Enter values for coordinates of the points into the text input fields
• Click the "Graph" button (this button can also be used to refresh the graph)
• The points can also be specified by using the mouse to click and drag the red points on the graph
• To reset the graph and all input fields to default values, click the "Clear" button
The text input fields can accept real numbers in decimal notation. The buttons under the graph allow various manipulations of the graph coordinates.
Examples
Shown here by the four points: (x1,y1) -- (x2,y2) -- (x3,y3) -- (x4,y4)
• "S" curve: (-1,-1) -- (4,-2) -- (-4,2) -- (1,1)
• Loop: (-1,-1) -- (4,2) -- (-4,2) -- (1,-1)
• Effect of tension: start with (-1,0) -- (-2,1) -- (2,1) -- (1,0)
change (x3,y3) (second control point) in steps:
1. (x3,y3)=(2,1) (start)
2. (x3,y3)=(3,2)
3. (x3,y3)=(4,3)
4. (x3,y3)=(5,4)
5. (x3,y3)=(6,5)
6. (x3,y3)=(7,6)

Other Notes
The graph goes through the endpoints (x1,y1) and (x4,y4), with (x2,y2) and (x3,y3) as "control points." The endpoints and control points for the Bezier curve are colored red in the graph, and the line segments between the endpoints and their corresponding control points (indicating tangent vectors at the endpoints) are colored green.