Exploratories   Linear Algebra

 Bezier SplinesThis applet introduces the user to the usage and mathematics of spline curves and includes a tutorial, exercises, and an interactive play space. Coordinate TransformationsThe Coordinate System Transformations applet teaches several concepts. The first is how a transformation applied to a coordinate system affects the axes of that coordinate system. Second, this applet shows how looking at only a very small portion of any curve produces a straight line (linear approximation) of that curve. Finally, this applet shows how a transformation of the coordinate system affects any objects within that coordinate system. Dot ProductThe Dot Product applet shows how the scalar dot product value of two vectors depends on both the vectors' lengths and the angle between them. It also demonstrates the dot product's property of rotational invariance. Editable equations are displayed, as are concept explanations and help text. The dot product is an essential building block in linear algebra and for doing almost any type of transformation or rendering in computer graphics. Normal Scaling 2DThe 2D Surface Normals applet shows students how surface normals are affected by non-proportional (non-uniform) scaling. Without this knowledge, the shading of non-uniformly scaled objects is often calculated incorrectly. Reflection 2DThe 2D Reflection applet is an interactive illustration letting users reposition a light source and automatically recalculate the reflection vector. The standard equation is used with N, L and R for, respectively, the surface normal, normalized direction to a light source, and normalized reflection of L off of a surface. All equations are automatically updated with a user's changes to the illustration. A series of tips/concept explanations are available.This applet helps enhance complete understanding of essential task. Transformation GameThis applet introduces the user to the usage and mathematics of two-dimensional transformations using a fun, interactive play space.