This document describes using augmented reality to enhance a physics experiment on pendulums. It defines augmented reality as computer-generated virtual objects superimposed on live camera images using fiducial markers and computer vision. It outlines the tools used to develop augmented reality applications, including fiducial markers, C++, OpenCV library, and OpenGL. It provides the mathematical formulas and procedures for camera calibration and 3D construction to precisely position virtual objects in the scene. Specifically, it details the steps to implement a pendulum experiment using OpenCV functions to find marker corners in images and calculate intrinsic and extrinsic camera parameters. The conclusion states that other science experiments will also be augmented and potential applications include face recognition and automatic paper grading.

1. Science Experiment Enriched by
Augmented Reality
Anish Patel
Undergraduate, Sophomore Student, Computer Science
Dr. Daniel Vrinceanu
Associate Professor, Department of Physics

2. What is Augmented Reality?
1. Augmented reality is a computer generated
virtual world objects like animal, civil
projects, and physics experiment
superimposed on live imaging acquired by
camera.
2. Precise positioning of these virtual objects
in the scene is obtained by attaching fiducial
optical markers to real objects.
3. computer vision is used to detect an
identify markers in the scene image.

3. Augmented reality objects can
be develop using:-
1. Fiduciary Marker is a point of
reference to create objects on
its surface.
2. C++ is a High level, procedural
and, object oriented
programming language which
help us to write complex
programs.

4. 3. OpenCV, computer vision library
helps us to develop Major
application in real world like
Augmented reality, Facial &
Gesture Recognition, Motion
Tracking, and Machine Learning.
4. OpenGL, rich graphics library for
rendering 2D and 3D vector.

5. Pendulum Augmented Diagram

6. Camera Calibration and 3D
Construction formula
• (X, Y, Z) are the coordinate of 3D points in
the world coordinate space.
• (u, v) = (x, y) are the coordinates of the
projection point in pixels.
• “A” is a camera matrix, or a matrix of
intrinsic parameters.
• (cx, cy) is the principal point that is usually
at the image center.
• (fx, fy) are the focal lengths expressed in
pixel units.
s 𝑚′ = A 𝑀′
or
s
𝑢
𝑣
1
=
𝑓𝑥 0 𝑐𝑥
0 𝑓𝑦 𝑐𝑦
0 0 1
𝑋
𝑌
𝑍
1

7. • The joint rotation – translation matrix [R|t] is called a matrix of extrinsic
parameters. It is used to describe the camera motion around a static
scene, or vice versa, rigid motion of an objects in front of a still camera.
That is, [R|t] translates coordinates of a point (X, Y, Z) to a coordinate
system, fixed with respect to the camera. Another way to represent 3D
construction formulas:

8. Procedure for Pendulum Experiment
with Computer Vision OpenCV
Library
• Calculate pixels of camera for matrix calculation.
Example:- /* add predefine library and some programming
statement */
VideoCapture video(0); // to read video from camera
Mat img = imread(“marker.png”,1); // to read image
height = video.cols;
width = video.rows;
Pixcel = height * width; // (like 8.5 cm* 8.5 cm)
• Convert color image to black and while
Example:-
cvtColor (src /* color image */, src_gray /* black and white
image */, CV_BGR2GRAY /* convert image */ )

9. • Find corner of marker in image.
Example:-
findChessboardCorners(inputArray image, size patternSize, outputArray
corner, int flags = CALIB_CB_ADAPTIVE_THRESH +
CALIB_CB_NORMALIZE_IMAGE)

10. Conclusion
• After developing the simple pendulum example
several other science experiments will be
augmented in the similar fashion. Other
applications of this technology include face
recognition and automatic paper grading.

11. Thank you !
Do you have any questions?