iNSIGHT Spatial Vision vs Drawing with Math

A process called Fourier analysis can be used to mathematically break down any image into a number of basic components. By manipulating these components and then reassembling them, a variety of visual effects can be achieved. This process demonstrates how our visual system analyzes images, and how different types of visual problems can affect our perception of shapes and edges. iNSIGHT is a curriculum supplement for experimental psychology, sensation and perception, vision science, and optometry lab classes. There are two different types of iNSIGHT apps: experiments and interactive demonstrations. Experiments are real psychophysical procedures (NOT simulations) that generate real data. Demonstrations illustrate a visual phenomenon and allow students to manipulate the effect. Each lab is complete with a quick-start guide, detailed instructions, background information, and one or more guided exercises. To see how iNSIGHT works, try the FREE iNSIGHT Color Mixing app. A printable PDF Student Guide that contains the exercises and other supporting materials, and a Teacher Guide are available at www.polyhedronlearning.com/see_apps_insight.html

Our “Drawing with Math (Vector and Pixel Art)” app combines two main components: * uniquely versatile image editors, * various methods of linear transformations of both user-entered and system images. Image editors are available in vector and pixelated forms. The editors offer such options as: * free drawing, * entry of all standard shapes, * entry of regular Cartesian, polar, or parametric function into image editor. List of several visually appealing functions is provided. The App stores 10 most recent user entries for each type. Vector images can be linearly transformed in a variety of user-defined ways: * 2x2 matrix, * eigenvalues and eigenvectors, * rotation by degree, * reflection across a given vector. Pixelated images can be compressed by segments to user-selected rank. Mathematical context for the above is provided, whenever possible. Explanation of image compression algorithms requires significant understanding of Linear Algebra, and is available in our “Matrix Solver Step by Step” app. Several bonus images with animations and editable greeting cards are also available. Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.