Perspective Definition and 221 Threads

Linear or point-projection perspective (from Latin: perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to foreshortening, meaning that an object's dimensions along the line of sight appear shorter than its dimensions across the line of sight. All objects will recede to points in the distance, usually along the horizon line, but also above and below the horizon line depending on the view used.
Italian Renaissance painters and architects including Masaccio, Paolo Uccello, Piero della Francesca and Luca Pacioli studied linear perspective, wrote treatises on it, and incorporated it into their artworks, thus contributing to the mathematics of art.

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  1. Z

    How to interpret the difference in height between two people in this Ames room?

    Homework Statement: From a description of the photo below, the woman on the left is actually taller than the boy on the right. Relevant Equations: This is a so-called "Ames room" and has been constructed to eliminate the usual monocular depth cues that our eyes use to determine distance based...
  2. M

    New member hoping to share a new perspectives!

    Hi I hope everyone has an open mind. I hope to share what may seem a bit much, as it will flip what we understand on its head. If you hear me out I think you will find it quite a thought provoking possibility. I look forward to your thoughts on my next post. Nice to be here and thank you for...
  3. wirefree

    I Is there a way to calculate this transformation?

    Namaste & G'day! Imagine a helicopter view of a Polo ground. It's length & breadth are known. Now you are seated where the blue dot is. Your view is such: How do mathematicians calculate the distance travelled by a ball from the second perspective? From the top view, this would be...
  4. S

    Calculating Time Dilation for Space Travelers

    If we took the perspective of the space traveller themselves, they are stationary and the whole universe goes past them at 0.7c. THen th elapsed time of 6.5 yr looking outside is \Delta t =6.5 \frac{1}{\sqrt{1-0.7^2}} = 9.11 yrs THen, when the traveller looks at the person travelling at 0.9c...
  5. G

    History Why Did Ancient Greeks Excel in Sculpture but Not in 2D Perspective Art?

    How is it that the early Greeks and Romans had such well-sculpted statues of human figures, but not so well-drawn people on canvas or other 2D surfaces?
  6. roshangomez

    Understanding Spatial Description: A Mathematical Perspective

    I understand the mathematical difference, that the independent variables are the "reference position vector+time" for material description, and "current position vector+time" for the spatial description. But I can't seem to wrap my head around the concept of the spatial description.
  7. lyra-stem

    From a teacher’s perspective, what gaps do you see in STEM education?

    Hello everyone! I’m a college student interested in starting a nonprofit organization centered around supplementing classroom STEM education. After working with a few schools and teachers in my area (Northern NJ), I’ve been told that students could benefit from more learning opportunities...
  8. P

    I Exploring Time Dilation: A Layman's Perspective

    According to a video I watched recently 'time' allegedly runs a tad slower in places on the Earth where the magnetic field is stronger. No doubt that has been tested and confirmed by atomic clock experiments.. to my simple mind that just suggests a timing error caused by the difference in...
  9. jisbon

    A Projection of 3D Plane from a certain perspective on the 2D Plane

    Hello all! As seen in the summary, I'm not sure if anyone can understand, but I will try to make this as clear as possible. Working in the 3D Plane: Given that there is a trajectory motion in the 3D Plane, and I have the coordinates of the motion at every 1s interval. This means at t=1s, the...
  10. Ravi Mohan

    What Are the Dimensions of Hilbert Space Elements in Quantum Mechanics?

    Hi Fellas! My first post after a long hiatus from forums. Feeling nostalgia (this is the place where it all began, my fuel for quantum fascination so to speak). I am revisiting the mathematical formulation of quantum mechanics with the dimensional (MLT) perspective. I want to understand what...
  11. O

    I Twin Paradox: Spacetime Physics Ch.4 & 202 Year Difference

    Spacetime physics chapter 4 describes this wonderfully well chosen set of speeds/distances for the twin paradox. A traveler departs from Earth at a speed of 99/101 (1=speed of light), traveling to a star that is 99light years away. From Earth's perspective, the traveler takes 101 years to go...
  12. S

    B Integration from "Area Under Curve" Perspective: Explained

    I can calculate the value of the integration, it will be ##\frac{\sqrt{3}}{2}## But if I draw the function and consider the area bounded by the curve and x-axis from x = 0.5 to x = 1, it seems that the area will be infinite because x = 1 is vertical asymptote. Why can't I consider from "area...
  13. M

    B When does the perspective from the cockpit of a spaceship change?

    Hi, Maybe this is a foolish question but I am not able to wrap my mind around it. I imagining a spaceship approaching the Earth as shown below. The ship is planning to land at the red cross in the first picture, somewhere in Europe. I think, from this distance the pilot must feel that he is...
  14. Killtech

    I The world from a bat's perspective (sonic images)

    Disclaimer: This will be a lengthy post and it will take me a little time to outline how this is related to this forum, so please hang in with me here please – and for everyone that makes it to the end, thanks for taking the time. So let’s start with the premise that we want to make a 3d game...
  15. Judah_Idris

    Classical Physics from a Rigorous, Experimental Perspective

    I have a physics B.S. It seems like I learned little more than how to solve math problems as an undergrad. I want to know how the physical world works in concrete physical terms as much as is possible, so a big problem I have with physics is that concepts are very often explained in terms of...
  16. K

    I Spontaneous symmetry breaking from a QM perspective

    Hello! This questions might not make sense and I am sorry if that is the case (I am asking from a QM class perspective). I am a bit confused about the idea of spontaneously symmetry breaking (SSB), from the point of view of QM. I am talking here about the energy plot looking like a mexican hat...
  17. P

    Special relativity, a non-inertial perspective

    I have tried calculating it as a Uniform Accelerated Movement problem: , where t is the time for the observer at Earth, O. For calculating t'' (the proper time for the accelerated spaceship observer), it is just using a Lorentz transformation? It seems easy, but as is stated that the frame is...
  18. jim mcnamara

    Change in perspective for Natural Selection

    https://phys.org/news/2020-01-fossil-upend-basic-tenet-evolutionary.html Sandra Catania et al. Evolutionary Persistence of DNA Methylation for Millions of Years after Ancient Loss of a De Novo Methyltransferase, Cell (2020). DOI: 10.1016/j.cell.2019.12.012 Using pathogenic fungus species, the...
  19. Huyanyinglei

    Issue with perspective projection?

    Summary: Perspective projection is often referred to when talking about camera models I have the following problem. Perspective projection is often referred to when talking about camera models(https://en.wikipedia.org/wiki/3D_projection#Perspective_projection). I don’t think I understand it...
  20. D

    B Why does the Andromeda galaxy appear so tiny from our perspective?

    Hi, and thanks for reading. I asked this question in another forum too. If we agree that Andromeda is 2.5 million light years away, and its diameter around 220,000 light years, I don't see how it just appears as a regular point of light like any other star in the unaided eye. Something that so...
  21. J

    B Gaining Perspective on Valid Digits in Physics Problems

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  22. T

    Programs Viability of International Degrees (from the US perspective)

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  23. mrSpring

    I Time Dilation Effects - Understand without Clocks

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  24. J

    A physics perspective needed on how the Mitochondria machine works

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  25. Kitty123

    Testing Perseverance And Perspective....

    I am an undergrad with a husband and 4 kids. I work, tutor, work in a lab... all on top of my classes. I do really well on homework (and I really enjoy sitting and deriving with my white board) and I do well on our weekly quizzes. I stay above the average mark on everything... except exams; I...
  26. R

    What if speed=time/distance? Torpidity

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  27. W

    B Is Lorentz Contraction Bona Fide or Just A "Perspective"?

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  28. S

    I Is perspective a homothetic transformation?

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  29. FallenApple

    I Energy perspective on deterministic intelligence

    This question is kind of out there, so I'm not sure where to put it. But it is physics, somewhat, under the fact that information itself contain energy. So, is it physically possible for a computer program running off of logical statements alone to be as intelligent as a human? Because this...
  30. Ricky Lalduhzuala

    B Feeling Earth's Rotation: A Teleported Alien's Perspective

    If someone from the outer space suddenly teleport to the Earth , will it feel the rotation of the earth? will it be disturbed by the fast rotating earth.
  31. Rob-NYC

    B Uniform motion and time dilation - real or perspective based

    Does time dilation in relative UNIFORM motion REALLY happen or is it merely a perspective from one reference frame relative to another as in the simple case where objects appear smaller the further away they are from the perspective of an observer in a particular reference frame? Putting it...
  32. D

    What is the angle of perspective for circles in a view of The London Eye?

    Good Morning everybody. I hope that this thread is of interest. I am a retired architect with an interest in Mathematics. My picture shows a view of The London Eye. We know that it views as an ellipse but the major axis (drawn), clearly is not at right angles to the axis of the wheel and if you...
  33. chastiell

    Is perspective distortion mathematically modeled?

    Hi guys ! I'm trying to understand the perspective distortion that can be observed in our vision and cameras, so many pages on the web that talks about photography says that the perspective distortion can be controlled using different focal lengths lenses, meanwhile a reduced group of pages...
  34. M

    The Bernoulli principle from the perspective of statistical mechanics

    Hi community, I have a question about the Bernoulli principle. From statistical mechanics the pressure in the ideal gas is independent of velocity. But in the case of the flow of an ideal gas in a channel, the pressure depends on the velocity. Where can I clarify this misunderstanding...
  35. Chronos

    B Nobel laureate perspective on the history, status and future of GR

    This paper offers a Nobel laureate perspective on the history, status and future of GR in the astrophysical regime - https://arxiv.org/abs/1609.09781, General Relativity and Cosmology: Unsolved Questions and Future Directions.
  36. T

    B From a 4D perspective would 3D infinity exist?

    From the perspective of a 4D observer would 3D infinity appear to exist? Why/why not?
  37. nnerik

    What is frequency from a photon's perspective?

    If a photon does not experience time, how can it change? Without change, how can it have frequency?
  38. SSGD

    Convert Perspective picture to Ortho picture for CAD

    I want to take a picture of an object. Then import the image into cad. And trace it. The issue I am having is the picture from the camera is a 3D perspective image. So it is impossible for me to trace in CAD. Is there a way to convert an image from perspective to orthogonal? Or create a...
  39. G

    Exploring Earth's Escape Velocity: A Non-Physics Perspective

    Hi, First FYI, I have no education in physics. Anyway - I know Earth's escape velocity is about 41,000 kph. Anything less, and you'll eventually fall down back to earth. Two points that seem to contradict each other - 1. Escape velocity gets decreased the farther away you are from the...
  40. The PAQI Monsta

    Choosing Between Queen Mary London, Sussex & Leicester: A Student's Perspective

    I have offers from Queen Mary London, Sussex and Leicester, but I think I'm leaning slightly towards Queen Mary. In terms of intensity, it seems Leicester is the most intense then QM then Sussex, based on the number of modules in each year. Is this something worth taking into account and how...
  41. lisab

    Historical Perspective of Queen Elizabeth's Rule

    This won't be news to the lovely PFers who happen to be Brits or Commonwealth citizens. But this floored me - I guess I'd never really thought about it: Several hundred years from now, people might not think of the latter part of the 20th century as the Cold War Era, or the Post-WW2 Era, or...
  42. F

    The relation between classical from quantum vs measurement perspective

    What is the relation between classical from quantum vs measurement problem. On one hand they seem to be related on the other they seem to be of different nature. We always see our screens on front of us and not 100 meters away, that we say is classical object although the screen is a quantum...
  43. S

    Understanding Big R(t) in Astronomy: A Physical Perspective

    I'm having trouble with with understanding what this is, our text, Astronomy: a physical Perspective by Kutner, uses R(t). I understand r(t) is the distance between two objects at a point in time, but what is the scale factor big R(t)?
  44. R

    Tree Trunk Illusion: Does it Disappear Over the Horizon?

    Supposed there is a tree on a perfectly flat plane. If an observer in front of that tree moves further and further away from the tree, the tree would look smaller and smaller. When the observer moves further and further away, would the lower part of the tree's trunk seem to disappear as if...
  45. I

    Inside a black hole, looking out

    I have been pondering black holes for some time and have had trouble with the problems presented simply because there is very little we can do to study the phenomena. I have always thought of a black from the outside looking in, or basically the only way we can hope to see a black hole. However...
  46. M

    Understanding the Metric Tensor: A 4-Vector Perspective

    Some subtleties of the metric tensor are just becoming clear to me now. If I take ##g_{\mu\nu}=diag(+1,-1,-1,-1)## and want to write ##\partial_\mu\phi^\mu##, it would be ##\partial_0\phi^0 -\partial_i\phi^i##, correct? ##\phi## is a 4-vector.
  47. Lamdbaenergy

    Visual perspective at the speed of light:

    I have been doing a lot of reading about this and it seems really, really interesting. Correct me if I am wrong on any of this, but I'm going to attempt to summarize how traveling at the speed of light, or at least 99.998 percent the speed of light, would look in two different cases: in...
  48. marcus

    Perspective on an historian/archeologist

    I recently became aware of the work of an Israeli historian and archeologist by the name of Israel Finkelstein who I gather is the director of the Institute of Archeology of the University of Tel Aviv. He is also co-director of the Megiddo archeological works (or "digs") and co-author with Neil...
  49. P

    From an evolutionary perspective, why would this happen?

    For those who believe human behavior is explicable in terms of evolutionary biology, can you please explain the following event. I'm personally at a loss for words. Maybe somebody else can help me make sense of this.
  50. S

    How BJT transistor works (with conventional current notation perspective)

    So far the explanation on BJT working principle always explained in electron flow perspective. I felt it's hard to relate with conventional current direction notation when the explanation explained in electron flow direction notation. For example in NPN transistor, the C-E current flow made me...
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