Laura received her Master's degree in Pure Mathematics from Michigan State University, and her Bachelor's degree in Mathematics from Grand Valley State University. She has 20 years of experience teaching collegiate mathematics at various institutions.
Orthographic Projection: Definition & Examples
Orthographic Projection
Suppose you want someone in another country to design this triangular structure for you. You send them this picture, but it causes some confusion.
Do they consider the green triangle to be in the front or the back of the structure? You don't speak their language, so you can't explain it to them. What do you do?
Thankfully, we have orthographic projections to help in situations like this. Put simply, an orthographic projection is a way of representing a three-dimensional object in two dimensions. It uses different two-dimensional views of the object instead of a single three-dimensional view. This allows you to communicate exactly what you want your structure to look like and eliminates any miscommunication between you and the person creating your design.
An error occurred trying to load this video.
Try refreshing the page, or contact customer support.
You must cCreate an account to continue watching
Register to view this lesson
As a member, you'll also get unlimited access to over 84,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.
Get unlimited access to over 84,000 lessons.
Try it nowAlready registered? Log in here for access
BackYou're on a roll. Keep up the good work!
Just checking in. Are you still watching?
Yes! Keep playing.Different Views
Typically, an orthographic projection drawing consists of three different views: a front view, a top view, and a side view. Occasionally, more views are used for clarity. The side view is usually the right side, but if the left side is used, it is noted in the drawing.
To draw one of the views of an object, use lines to represent changes in depth. For example, consider this object with its right side view orthographic projection:
Notice that there are lines where there are any depth changes in the structure; this changes the right side view of a three-dimensional object into a two-dimensional picture. These next two images show the front view and the top view of the same object:
Measurements
In an actual orthographic projection, all of the views are included on the same page. Normally, the front view is in the lower left corner of the page, the top view is in the upper left corner, and the right side view is in the lower right corner. The same scale is used for all three of the drawings, and their lengths, widths, and heights are all lined up.
Sometimes, the isometric drawing of the object is included in the upper right corner. An isometric drawing is a view of an object from a corner angle so that all the different views of the object can be seen. Though an isometric drawing is two-dimensional, it appears three-dimensional. The isometric drawing need not be drawn to scale or lined up with the three orthographic projection drawings.
Often, an orthographic projection drawing includes measurements of the dimensions of each of the views. This allows the person creating the design to make it to scale as the designer wishes. This image shows the actual orthographic projection of the object shown earlier:
Example
Let's consider another example. Suppose you want to build a set of steps that you can use to reach the top shelf of a cupboard. You know there are three steps, and you know how tall the steps need to be and the dimensions of each step. The only problem is that you can't build them yourself. The good news is that you can create an orthographic projection of your steps and present it to a builder, and they can build it for you based off your orthographic drawing shown in the image:
In the image, we see that you want a set of steps that are each ten inches high, twelve inches deep, and 36 inches long. This shouldn't be too hard for the builder to make. You will have your set of steps in no time thanks to this drawing!
Lesson Summary
Orthographic projections are two-dimensional drawings of different views of a three-dimensional object. These projections serve as a sort of universal language when it comes to engineering and building, and allow for smooth communication between designer and builder as to what is expected.
An orthographic projection normally contains three views of the object: the front view in the lower left corner, the top view in the upper left corner, and the right side view in the lower right corner. The drawing often includes an isometric drawing of the object, which is a view of the object from an angle that shows all three of the different views. Measurements and dimensions are also normally included in the drawing. Orthographic projections are extremely important in mathematics, engineering, and the like, so it's great to be familiar with them.
To unlock this lesson you must be a Study.com Member.
Create your account
Register to view this lesson
Unlock Your Education
See for yourself why 30 million people use Study.com
Become a Study.com member and start learning now.
Become a MemberAlready a member? Log In
BackOrthographic Projection: Definition & Examples
Related Study Materials
- Math Courses
- Standardized Tests Courses
- Test Prep Courses
- Study Courses
- State Exams for K-12 Students Courses
- Algebra Connections: Online Textbook Help
- Discovering Geometry An Investigative Approach: Online Help
- GED Study Guide
- NYSTCE Business and Marketing (063): Practice and Study Guide
- Veterinary Assistant Exam: Prep & Study Guide
- Holt McDougal Larson Geometry: Online Textbook Help
- ASVAB Mathematics Knowledge: Study Guide & Test Prep
- ACT Writing Test Practice
- ACT Science Section: Prep & Practice
- ACT Reading Section: Prep & Practice
- ACT Math Prep: Review & Practice
- CBEST Reading: Practice & Study Guide
- McDougal Littell Algebra 2: Online Textbook Help
Browse by Courses
- Roman Plebs: Definition & Overview
- Satyr Play: Definition & Overview
- Tartarus of Greek Mythology: Definition & Explanation
- The Ancient Gauls: History & Explanation
- The Ancient Roman Calendar: History, Months & Saints
- Quiz & Worksheet - Using Notation to Understand Limits
- Quiz & Worksheet - The Properties of Limits
- Quiz & Worksheet - One-Sided Limits and Continuity
- Quiz & Worksheet - Determining the Limits of Functions
- Quiz & Worksheet - Using the Squeeze Theorem
- The Science Learning Environment
- FTCE Middle Grades General Science 5-9 Flashcards
- Praxis English: Literary Forms and Genres
- Literary Skills & Strategies
- Praxis English: Analyzing Literature
Browse by Lessons
- Biology 202L: Anatomy & Physiology II with Lab
- Biology 201L: Anatomy & Physiology I with Lab
- California Sexual Harassment Refresher Course: Supervisors
- California Sexual Harassment Refresher Course: Employees
- Sociology 110: Cultural Studies & Diversity in the U.S.
- Everyday Math Skills
- Skeletal System Function and Parts
- Muscular System Anatomy and Movement
- Reproductive System Functions and Anatomy
- Cardiovascular System Function and Parts
- TExES Principal Exam Redesign (068 vs. 268)
- Teacher Salary by State
- ESL Resource Guide for Teachers
- What is a Homeschool Co-op?
- How to Start Homeschooling Your Children
- Addressing Cultural Diversity in Distance Learning
- New Hampshire Homeschooling Laws
Latest Courses
- The House of the Seven Gables: Themes & Analysis
- Animal Lesson for Kids: Definition & Characteristics
- Polar Coordinates: Definition, Equation & Examples
- A Newspaper Story by O. Henry: Summary & Analysis
- Setting of The Old Man and the Sea: Description & Importance
- Characterization in Wuthering Heights
- Component-Level Design: Steps & Examples
- Quiz & Worksheet - Income Capitalization Approach in Real Estate
- Quiz & Worksheet - Net Operating Income & Gross Rent Multiplier
- Quiz & Worksheet - Calculating the Probability of Chance
- Quiz & Worksheet - Determining Entity OwnerÂs Basis in C Corporation Stock for Federal Income Tax
- Flashcards - Real Estate Marketing Basics
- Flashcards - Promotional Marketing in Real Estate
- Digital Citizenship | Curriculum, Lessons and Lesson Plans
- Narrative Essay Topics for Teachers
Latest Lessons
- Nutrition 101: Science of Nutrition
- 12th Grade English Textbook
- High School Algebra II: Help and Review
- College English Composition: Help and Review
- High School Algebra I: Homework Help Resource
- AP European History - The Age of Expansion: Tutoring Solution
- Analytic Methods in Genetics for the MCAT: Tutoring Solution
- Quiz & Worksheet - George Miller's Short Term Memory Theories
- Quiz & Worksheet - Forming Relationships With a Career Mentor
- Quiz & Worksheet - Headers, Footers & Slide Numbers in PowerPoint
- Quiz & Worksheet - Aligning Group Shapes in PowerPoint
- Quiz & Worksheet - The Steps of Family Counseling
Popular Courses
- Secure Attachment Style: Definition & Examples
- What Is HDL Cholesterol? - Definition & Healthy Levels
- Fairfield, CA Adult Education
- One Grain of Rice Lesson Plan
- International Baccalaureate vs. Advanced Placement Tests
- Is AP Environmental Science Hard?
- Palo Alto Adult Education
- Math Card Games for Kids
- What is CDT Certification?
- What GPA Do Colleges Look At?
- Script Writing Prompts
- HRCI Online Recertification & Continuing Education Credit
Popular Lessons
Math
Social Sciences
Science
Business
Humanities
Education
History
Art and Design
Tech and Engineering
- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers
Health and Medicine
- Consider the following vectors \vec u = \langle 2, -6, -7 \rangle , \vec v = \langle 5, -1, -8 \rangle (a) Find the projection of \vec u onto \vec v . (b) Find the vector component of \vec
- Let a = (-4, -9, 0) and b = (2, -1, -8) be vectors. Find the scalar, vector, and orthogonal projections of b onto a .
- Find the orthogonal projection of [- 11 6 - 18 - 17] onto the subspace W spanned by { [2 - 1 5 1], [- 1 2 - 2 4] }. proj_W(vec{v}) = [ ]
- Let y={4} \\ {-6} \\ {4}\ , u_{1}={r}{-3} \\ {-4} \\ {1}\ , u_{2}= \{r}{-1} \\ {1} \\ {1}\. Find the distance from y to the plane in \mathbb{R}^{3} spanned by u_{1} and u_{2}.
- Use the inner product \left \langle f,g \right \rangle = \int_{0}^{1} f(x)g(x) dx in the vector space C^{\circ}\left \langle 0,1 \right \rangle of continuous functions on the domain \left \langle 0,
- Find another vector that has the same orthogonal projection onto v = <1, 1> as u = <1, 2>. Draw a picture.
- a. Which of these are unit vectors: \vec{a} = (1, 2), \vec{b} = (- \frac{1}{2}, \frac{\sqrt{3}}{2}), j? b. Compute the following vector projections, using the vectors from the previous problem: proj
- Suppose \mathbf u=( - 3, 1.,4) and \mathbf v( - 2. -2. 5). Find projection of \mathbf u along with \mathbf v and the projection of \mathbf u orthogonal to \mathbf v.
- For the vectors a = (1, 4) and b = (2, 3), find orth_ab.
- For the vectors a = (1, 4) and b = (2, 3) find orth_a b.
Explore our library of over 84,000 lessons
- Create a Goal
- Create custom courses
- Get your questions answered