Questions tagged [projections]

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Projection of line which lies in an auxiliary inclined plane

A line PQ is 75 mm long and lies in an auxiliary inclined plane (A.I.P.) which makes an angle of 45° with the H.P. The front view of the line measures 55 mm and the end P is in the V.P. and 20 mm ...
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OpenGL old-style diffuse shading producing unexpected effects

Question: What is going wrong with the shape of the contours of constant illumination in the below picture ? Detail: Although Lambertian shading might be ill-regarded because it exposes the hard edges ...
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1answer
118 views

3D homogenous coordinates versus 4D homogenous coordinates

We know that any 2D point $(x, y) $which represents as 3D homogeneous coordinates is of the form $(x, y, 1)$ which is the points of projective plane $P^2.$ If I use the same concepts for 3D points $(...
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2answers
145 views

$(x, y, 1)$ is 2D homogenous coordinates or 3D homogenous coordinates?

We know that $(x, y, 1)$ are the homogenous coordinates of a 2D point $(x, y)$. $(x, y, 1)$ has 2 degrees of freedom. That's why we should call it 2D homogenous coordinates. But many websites say it's ...
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1answer
64 views

Finding a texture pixel (X,Y) on a Sphere

I'm using three.js combined with face recognition, I want to rotate a sphere that displays my input video according to the detected eye location, the face recognition gives me a X,Y on the texture ...
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1answer
146 views

Perspective transformation is perspective projection? [duplicate]

I know that ( Reference )in transformation source and destination has same coordinates dimensions. But in projection destination coordinate system has fewer dimensions than the source coordinate ...
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5answers
962 views

Existence of vanishing point

Consider the following example of perspective projection: I have one railway track with two parallel lines meeting at the point $X$ at infinity which is the theoretical approach. This X is called the ...
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0answers
51 views

3D shearing w. r. t $x$-axis [closed]

Shearing in $X$ axis is achieved by using the following shearing equations- $X_{new} = X_{old}, Y_{new} = Y_{old} + Sh_y × X_{old}, Z_{new} = Z_{old} + Sh_z × X_{old}.$ My question is during $Y_{new}...
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1answer
158 views

Difference between 2D and 3D pipeline

2D transformation and viewing: The camera projects the 2D world co-ordinate $(x_w, y_w)$ on its projection plane which co-ordinates $(x_v, y_v)$. 3D transformation and viewing: The camera projects the ...
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1answer
96 views

Parallel projection is special case of perspective projection

I synchronized with @David k's first and second answer regarding perspective and parallel projection. From the first question I understand that the image on the screen is typically described in ...
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1answer
119 views

Difference between transformation and projection? [closed]

We know that world coordinates $(x_w, y_w)$ transform to viewport coordinates $(x_v, y_v)$ which are the physical device coordinates. And during projection, any point $(x, y, z)$ projects to $(x, y)$ ...
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1answer
70 views

Why shearing coefficients multiplying by y? [closed]

We know that shear is transformation that distorts the shape of the object. Shear relative to X-axis that is $y=0$ line can be written as: $x'=x+sh_x.y, y'=y$ My question is why $sh_x$ is multiplying ...
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2answers
111 views

Difference between perspective and parallel projection [closed]

We know that in orthographic Projection Projectors (projection vectors) are perpendicular to the projection plane. And in Perspective Projection Object positions are transformed to the view plane ...
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1answer
162 views

Why are vanishing point and centre of projection the same [closed]

We know that in perspective projection object positions are transformed to the view plane along lines that converge to the projection reference (center) point like this: But many websites say that COP(...
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1answer
149 views

$P^2$ vs projection plane

I want to explain what I understood of definition of the two things. Projection plane: The general processing steps for modeling and converting a world coordinate description of a scene to device ...
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0answers
61 views

Mapping an image from one camera pose to another given a planar scene

I'm trying to map an image of a 3D object to another one from a different camera position. My assumption is that the pose change between two cameras is so small and the object is far enough from the ...
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0answers
39 views

What should be considered the origin of a ray used for object picking with perspective projection

I need to create a ray to pick objects in 3d environment using cursor. I'm not going to go into detailed math for this question. There's tons of information on that. In short terms, for orthogonal ...
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1answer
115 views

How does 3D graphic software adjust for distortion inherent in perspective projection?

As this question and its answers point out, projecting a sphere on a flat picture plane, with perspective projection, may result in a ellipse, not a circle, and my understanding is that the only way a ...
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1answer
88 views

how to change the near clipping plane of a perspective projection matrix for OpenGL

I am trying to only change the near clipping plane of a given perspective projection matrix for OpenGL. My problem is, that the near clipping plane is way too close, and the far clipping plane is very ...
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0answers
18 views

Determining camera pose from symmetrical points?

I'm trying to do some 3D reconstruction from photographs and "the usual (SfM) suspects" don't seem to be working out. (Also, while I have a pretty good grasp of the basics of Linear Algebra, ...
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0answers
27 views

Writing perspective transformation matrix for x=0?

I see the discussion at this link, but I still get confused and I think my question is rather a simple one. If I assume the center of projection as p = (1,0,0), how can I write the 4x4 projection ...
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2answers
154 views

What is this graphical effect called?

I was watching this trailer: https://www.youtube.com/watch?v=pWh5388AEHw and at 1:22, the player used a magic trick that created a sphere that warped the projection of the scene. Does anyone know ...
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0answers
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Bottom up (as opposed to top down) text on projective geometric algebra?

I have been reading the SIGGRAPH course notes on projective geometric Algebra, and I get some of what's going on. However a lot of the knowledge needed to understand these PGA notes seems to be based ...
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57 views

computing sheared perspective projection matrix

is it possible to calculate a "projection matrix" which is sheared as well? the usual perspective projection matrix forms a pyramid where the near clipping plane is rectangular. I have 4 ...
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1answer
311 views

is focal length equal to the distance from the optical center to the near clipping plane- openGL

The part confusing about opengl during studying the projection was that the focal length, top, left, bottom, right, wasn't declared, and it magically did it with FOV and image aspect ration. I ...
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1answer
37 views

Moving a vertex through the cursor

There is a way to move a selected point in a mesh with a cursor(assuming a camera that doesn;t change between frames). The way I remember the algorithm (but seems to be wrong) is: Unproject the ...
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1answer
31 views

Does angular diameter to FoV ratio equal object's image to total image ratio?

If we have an object at certain distance D in front of a camera. The object has a horizontal diameter d, giving us an angular diameter theta (2*arctan(d/2D)) of 50 degrees (converted from radians). ...
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0answers
92 views

Project grid on 2d plane based on camera perspective

Unsure if this is the right network to post this, but maybe someone can help... I'm working on a personal project where, with the help of AI, I want to automatically estimate the perspective of a ...
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0answers
49 views

What is the best way to calculate the projected size of a point

In a particle simulation, I am rendering particles as "spheres" using GL_POINTS instead of a mesh for efficiency. With glEnable(GL_PROGRAM_POINT_SIZE) I ...
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0answers
104 views

Model View Projection Matrix Multiplcation Order

I'm working on a simple software renderer and have a working implementation so far. I'm curious as to why it's actually working since I would expect the multiplication ordering for my world, view and ...
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39 views

Can surface normal be used for obtaining points on a plane?

Excuse my wording. I will use the picture below to explain what I mean. I want to use the surface normals for each arrow shown like below to draw lines parallel to each plane like the image shown ...
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1answer
212 views

How are textures projected onto 3d models in texture painting applications

In most modeling software you can texture paint onto 3d models using so called stencil textures. They basically project a texture from the viewport view onto the model as seen for instance in the ...
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1answer
111 views

How is orthographic projection used in computer graphics technically classified as a projection?

I'm wondering why the orthographic projection we use in computer graphics is called a projection, if all it does is just scale and translate a mesh? According to wiki orthographic projection is ...
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1answer
484 views

Perspective correct interpolation z-buffer

While I was deriving expressions for perspective-correct linear interpolation on triangles, I reached the conclusion that the interpolation may be kept linear only if view-space $Z$ is available. ...
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0answers
84 views

Why does my self-written rendering engine make further away objects look larger?

I am writing a very simple rendering engine. I have already made a few tests, but somehow the images it creates look wrong. Objects that are further away from the camera look larger than objects ...
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1answer
990 views

How to unproject cursor with orthographic projection

With perspective projection we can unproject screen space coordinates of the cursor to the near and far plane of the frustum and calculate the direction of the ray through the cursor. ...
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Consistent Video Depth Estimation from Monocular Lens to approximate LiDAR?

If the iPhone had LiDAR sensors, it would be possible to generate a 3D point cloud that you could theoretically use to furnish a 3D AR reconstruction of your surroundings. E.g. you could create an AR ...
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Does rotating object inside unit cube [-1,1] by homogenous matrix move it outside unit cube

I am just trying to rotate my pointcloud object which is inside the unit cube ([-1,1] in all x,y,z axis). What I did is use the basic rotation matrix from wiki and extend it to homogenuous 4x4 matrix (...
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1answer
70 views

Keep constant number of visible circles in 3D animation

I have created a 3D animation with a perspective projection of white circles moving randomly in a fake 3D space projected on a 2D computer screen (GIF 1). Since I need to keep the same number of ...
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3answers
810 views

perspective matrix derivation

Now there has already been an answer here in this stackexchange, but I don't understand certain aspects of it. The author has MORE DETAILED DESCRIPTION HERE(#1) but the problem is he doesn't describe ...
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0answers
261 views

how is zooming done in computer graphics

Since a projection plane and a center of projection is used for achieving perspective projection, the shape of the view frustum doesn't change changing the focal length(which is the distance from the ...
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1answer
85 views

Y axis inversion in 3D rasterization

What is the correct way to invert the y axis during the 3D projection? I see a lot a people doing: ...
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0answers
434 views

Intrinsic Matrix vs Perspective projection matrix

I was going through the camera matrix explained in the wikipedia article and understand how the matrix K \begin{bmatrix}f_x&s&x_0\\0&f_y&y_0\\0&0&1\end{bmatrix} is built. The ...
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1answer
153 views

Understanding the near clipping plane

I don't understand something about the near clipping plane. It's there to avoid the division by $0$ but when we compute the pixel coordinates, we just need to multiply by the clipping plane to clip ...
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0answers
49 views

Project a Square as rectangle in projection plane using perspective projection

Consider a square S with vertices (1,1,0), (1,-1,0), (-1,-1,0) and (-1,1,0) and a plane P defined by $z=1$. Let the perspective projection of S on P is denoted by S'. What coordinates of the Center ...
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0answers
63 views

How to Pan Zoom a spherical camera?

I asked this in regular SO but I think people are not understanding the question so i will try here: So, for anyone familiar with Google Maps, when you zoom, it does it around the cursor. That is to ...
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1answer
137 views

Why is the z direction away from the screen/viewer?

I wonder what is the reason that when z increase, the objects appear far away and when z is negative, the object is behind the camera?
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How combine multiple projections into a single pass?

We have a projector type display used in an automotive application, where a projector displays an application on the windshield. Because the projector would normally warp a flat image, we have to ...
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2answers
71 views

3d Math Primer book equation derivation - Projecting One vector onto another

I'm reading the book 3d Math Primer for Graphics and Game Development 1st edition by Fletcher Dunn and Ian Parberry. On page 61 there's this: How does it derive $ v_{||} $ there? It doesn't follow ...
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Projecting a point on a Freefrom surface

My first issue is getting a set of planes and a set of points as input, an find the projection of the those points on the nearest plane. That was pretty easy, where i just calculate the normal of the ...