3D Reconstruction of Graph Objects, Scenes, and Environments

Introduction

The new renaissance, is it here? The big wave of change, attributable to technology innovations, is it here? Growing technology advancements have provided expansions in unattainable areas for humanity. The world of education today is challenged by the growing number of modernized techniques available to facilitate recreating live settings for educational purposes. We are only a couple of clicks away from creating real world settings to enhance our teaching and learning processes. The latest visual trends in Hollywood and Bollywood have introduced and showcased three dimensional (3D) visual effects to captivate audiences by providing settings closest to reality: the reel world is enhanced to recreate real worlds. Furthermore, educational videos for children and adults comprise of teachable games and simulations that show clear improvements in providing insights into improved educational purposes. Behind these great technological, virtual advancements are sound mathematical / geometrical principles.

All over the world students are perplexed when dealing with numeric concepts (Trentacosta & Kennedy, 1997). Educators have dedicated a lot of time and resource in trying to find techniques and strategies to revive student interest in numeric concepts. Currently, many educators have been using pictures, videos, games, and simulations to stimulate individual interests in math. Mathematicians and statisticians are facing the dilemma of finding means and tools to stimulate individual interests when interpreting mathematical concepts and statistical graphs (Kosslyn, 1994; Macdonald-Ross, 1977). One strategy that authors are constantly debating is the use of charts. Numerical data can be communicated via chart (Meyers, 1970). For example, language is communicated via words, music via dots, graphic via visuals, and math via symbols. Similarly, when we speak, we use verbal embellishments; simple/complex words, poems, stories, and narration. Likewise, when we use illustrations, we are using visual embellishments, that is, through pictorial representation in the form of charts, 3D objects, 3D scenes, and 3D environments (Kosslyn, 1994, Chikatla, 2010).

Charts have been used for ages as a tool to communicate data for problem solving and decision making (Meyers, 1970). Charts are combinations of lines or pictorial forms of columns, bars, or pies that stand for ideas (East, 1952; Pettersson, 1993). Charts have the ability to very effectively show factual data. They help gain audience attention; and are explanatory drawings. They can help make predictions over time showing projections of future possibilities (East, 1942; Meyer, 1970). The visuals, plotted relations, words, and numbers collectively aid in the comprehension, saves the reader’s time, which also enhances communication of concepts provided. Quality charts require fewer explanations and as a result need less time to comprehend (Tufte, 1983). As such, many educators are communicating math concepts and data via charts (White, 1984). Additionally, the flexible nature of charts allows their design process to be easier. According to Spence and Krizel (1994), both children and adults demonstrate success in math learning when exposed to chart data.

In a small group survey conducted by Chikatla (2010), several individuals (Americans and Indians) indicated that pictorial chart images containing 3D objects, scenes, and environments could have made vast differences when comprehending mathematical concepts during their Graduate Record Examination (GRE). In this research, it was also found that participants did not have any problem comprehending when using either 3D pictorial or 2D traditional charts. In another research done by Dempsey, Chikatla, and Inpornvijit (2008) it was found that participants that used charts that included 3D objects and scenes performed better on multiple choice questions compared to their counter parts that used traditional two dimensional (2D) charts. Thus, for this chapter, we are going to focus on the value of reconstructed 3D charts for comprehending math concepts.