Bezier Surface Generator - 4 x 6 grid - Spreadsheet entry.[br]Note that a reasonably fast computer is required to run this model. Developed on HP i7, 8GB [br]RAM. Hiding "Surface" during input of data may overcome slowness. [br][br]By selecting appropriately from a grid of 4 rows of 6 points this model creates a system of [br]bezier curves from which is generated a surface having a boundary that may be rectangular, [br]triangular, waist-like or bulbous. For each of the 4 rows of the grid, from 1 to 6 points may be [br]chosen to be included in shaping the surface. Point selection proceeds in sequence from point [br]A1 (B1,C1, D1) through to A6 (B6, C6, D6) and is achieved by operating sliders [math]m_1,m_1,m_2,m_3[/math]. [br] The value of the slider corresponds to the degree of the bezier applied to a row: 0 (a point), [br]1 (straight line), 2 (quadratic bezier) and 3 (cubic bezier), etc. Having the "degree" (or power) [br]of each of the four lateral beziers alterable leads to the ability to create irregular shaped [br]boundaries. The x, y, z values of each point are introduced via the Spreadsheet. Although not [br]implemented here, the spreadsheet could be used to transform polynomial parametric [br]functions of up to power 5 into Bezier Control Points corresponding to that function, enabling [br]the modelling of recognised curves. [br][br]Points not included in the generation of the surface are blanked out on the screen.[br][br]Bezier curves have been limited to lie between their two end points. Accuracy falls away when [br]the curve continues beyond these limits. Never-the-less Slider limits are alterable.[br][br]Non-rational Beziers are at the foundation of this model although Rational Beziers could be [br]implemented, having the advantage of being capable of describing a greater range of curve [br]types (a circular arc is one such curve).[br][br]There are four levels to implementing this model and it was found necessary to describe the [br]surface by using only functions, functions of functions, ........... Although the shorthand [br]mathematical definition of a Bezier Surface is given by a [math]\sum\sum[/math][.......] notation, this [br]is not understood by Geogebra.[br][br]Background. A Bezier Surface is the trace of a point running along a single "longitudinal" bezier [br]curve whose Control Points are themselves points on "lateral" bezier curves. In this model the [br]degree of the longitudinal bezier is always three, requiring four such lateral bezier curves. The [br]trace-point on the longitudinal bezier has its position controlled by parameter "v" while [br]parameter "u" applies to the 4 lateral beziers. The degree of each of the four lateral beziers is [br]individually set by a slider ([math]m_0,m_1,m_2,m_3[/math]) to: 0 (a point), 1 (straight line), 2 (quadratic [br]bezier) and 3 (cubic bezier) etc.