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Course: Precalculus (Eureka Math/EngageNY) > Unit 2
Lesson 7: Topic E: First-person video games—projection matrices- How one-point linear perspective works
- Linear perspective interactive
- 1. Ray tracing intuition
- 2D rendering intuition
- 2. Parametric form of a ray
- Parametric ray intuition
- 3. Calculate intersection point
- Solve for t
- 4. Using the line equation
- Ray intersection with line
- 5. 3D ray tracing part 1
- Ray intersection with plane
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Linear perspective interactive
Interactive created by Phil Fulks
The colorful buttons at the top left hide or reveal elements
"A" allows you to adjust the transversals and your vantage point
"B" allows you to adjust the orthogonals
"C" allows you to adjust the upper transversals
"D" allows you to adjust the second vanishing point along the horizon line
"VP" allows you to manipulate the vanishing point along the horizon line
"A" allows you to adjust the transversals and your vantage point
"B" allows you to adjust the orthogonals
"C" allows you to adjust the upper transversals
"D" allows you to adjust the second vanishing point along the horizon line
"VP" allows you to manipulate the vanishing point along the horizon line
When Brunelleschi (re)discovered linear prespective circa 1420, Florentine painters and sculptors became obsessed with it, especially after detailed instructions were published in a painting manual written by a fellow Florentine, Leon Battista Alberti, in 1435. John Berger, an art historian, notes that the convention of perspective fits within Renaissance Humanism because "it structured all images of reality to address a single spectator who, unlike God, could only be in one place at a time." In other words, linear perspective eliminates the multiple viewpoints that we see in medieval art, and creates an illusion of space from a single, fixed viewpoint. This suggests a renewed focus on the individual viewer, and we know that individualism is an important part of the Humanism of the Renaissance.
Want to join the conversation?
- This is wonderful! It really shows how just a few small changes can radically change the viewer's perspective on the room - while still looking completely realistic!(31 votes)
- Yes, this is the best resource ever, to show how position and perspective are represented differently on paper. Fantastic!(4 votes)
- What do "V", D", and "H" stand for?(11 votes)
- V is for vanishing point; H for horizon and D is for the diagonal lines(12 votes)
- If I wanted the tiles on the floor to represent perfect squares ( not rectangles that sort of look like squares) what method would I use to achieve this?(4 votes)
- The videos on Linear Perspective here do not go into the observer and how they relate to the measuring point, which dictates the distortion of foreshortened space. You may wish to create a standard lens if you want the squares to feel square and not rectangular. Standard lens is generally accepted as between 35mm and 65mm, depending on the crop factor. You can calculate the proper lens type by creating a cone of vision, which also can only be calculated from the station point. This will tell you how distorted or not distorted your foreshortening will be. Once you have a canvas that resides within the cone of vision that will give you the lens that you desire, you must maintain the position of the station point, relative to the horizon line, relative to your vanishing point(s), relative to your measuring point(s) for the entire picture. Otherwise you must start over because changing these points will change the perspective.(4 votes)
- How about a programmer's perspective (no pun intended), and perhaps we could see the source code?(5 votes)
- What kind of math can be done with linear perspective?
Any matrix algebra?
How can we take a real view out the window and estimate the length of the VP if we were to make a sketch?(3 votes) - What does "orthogonal" mean?(2 votes)
- Orthogonal lines are perpendicular to each other; they meet at right angles.(3 votes)
- Does "D" (the 2nd Vanishing Point or Distance Point) move the single viewer closer/farther from the object?(3 votes)
- It's like changing the lens on your camera to give you a wider or narrow field of vision thus the appearance of either deepening or flattening the viewed space.(2 votes)
- Does anyone really think this stuff is important anymore?(3 votes)
- so what was the point of the 2nd vanishing point?(2 votes)
- It is used to calculate foreshortening. It is generally referred to as a measuring point even though it is referred to as a distance point here. It is calculated as follows: "the measuring point is the same distance away from the vanishing point, along the horizon line, that the vanishing point is to the observers eye. Once you have a station point, picture plane, and vanishing point in top view, just measure the distance from the vanishing point to the station point(observers eye). Then take your ruler, place the zero end on the vanishing point, lie the ruler along the horizon line, and make a mark on the HL at the extent of the distance you measured prior. Or, take a compass, place the metal end on the vanishing pint and the pencil end on the station point (observers eye) then swing the graphite end over to the horizon line and make a mark. This is your measuring point used for foreshortening the scene. This point will cross any orthogonal at the measure bar. The measure bar is necessary and needs to have equal units for this to work. Otherwise you will no longer have proportional squares for which to calculate.(2 votes)
- I learned about linear perspective a long time ago, but every time I draw something (using either 1 or 2 vanishing points) the result always feels less than authentic.
So now what I'd like to do is draw a picture of my living room. It is basically a rectangle, and I want to position myself at a very specific point in the room. So I know the exact dimensions, and the distance between me and the wall opposite to me, and my eye height. However, I do not know how to faithfully translate the distance between me and said wall on paper.
I could start by drawing the opposite wall to scale, but then how do I determine how wide the absolute bottom line on my paper should be that represents the floor where I am standing? Is there a way to calculate this? I have Alberti's schematic, but it doesn't tell me how to get the right distance between the wall and myself.(2 votes)