Affine Transform in PDF - pdf

I seem to be missing something related to how Affine Transform works in PDF. I have a requirement to do below -
A shape whose bottom-left edge located in origin
Rotate the shape to 90 deg Counter-Clockwise
Translate the shape to the destination
Now, when i apply affine transform, i am not getting the proper placement of the shape in the destination. After several experiments, i found that PDF Engines apply rotation AROUND the bottom-left corner of the shape as reference, but most literature guides rotation about the center axis, suggesting no difference would occur doing either way.
But i am not able to get correct arithmetic behind my transform ad i am unable to achieve the result. I am not very sound in Mathematics, hence, would appreciate any help in achieving this.
Prepare some illustrations to show how i am doing the transform.
My understanding of the math behind the transform may be wrong altogether and would appreciate if i can get some guidance. I am using PDFBox to achieve the same. Thanks in advance.

Related

GODOT: What is an efficient calculation for the AABB of a simple 3D model from a camera's view

I am attempting to come up with a quick and efficient means of translating a 3d mesh into a projected AABB. In the end, I would like to accomplish something similar to figure 1 wherein only the area of the screen covered by the cube is located inside the bounding box highlighted in red. ((if it is at all possible, getting the area as small as possible, highlighted in blue, would increase efficiency down the road.))
Figure 1. https://i.imgur.com/pd0E20C.png
Currently, I have tried:
Calculating the point position on the screen using camera.unproject_position(). this failed largely due to my inability to wrap my head around the pixel positions trending towards infinity. I understand it has something to do with Tan, but frankly, it is too late for my brain to function anymore.
Getting the area of collision between the view frustum and the AABB of the mesh instance. This method seems convoluted, and to get it in a usable format I would need to project the result into 2d coordinates again.
Using the MeshInstance VisualInstance to create a texture wherein a pixel is white if it contains the mesh instance, and black otherwise. Visual instances in general just baffle me, and I did not think it would be efficient to have another viewport just to output this texture.
What I am looking for:
An output that can be passed to a shader informing where to complete certain calculations. Right now this is set up to use a bounding box, but it could easily be rewritten to also use a texture. It also could be rewritten to use polygons, but I am trying to keep calculations to a minimum in the shader.
Certain solutions I have tried before have worked, slightly, but this must be robust. The camera interfacing with the 3d object will be able to move completely around and through it, meaning at times the view will be completely surrounded by the 3d model with points both in front, and behind.
Thank you for any help you can provide.
I will try my best to update this post with information if needed.

How to make edge sloped on a cylinder?

I'm beginner at 3D modelling and I'm making an office chair. Now I'm stuck at wheel area as I need a sloped edge cylinder for the base of the wheel.
Concept: The wheel is attached to a cylindrical base which is attached to the foot of the chair.
Current Situation: I draw foot of chair, made a circle on it and transformed into a cylinder. The end edge of the cylinder has no Face and I want to extrude the cylinder along one edge which will make a sloped area on the open side of area. That should look like this :
But I tried manythings to do, but failed. It's obvious as I said I'm beginner. Please help me do to this.
Note: I'm using blender 2.78
The shear tool will move your mesh the way you want. It doesn't create the geometry so first extrude E and then shear ⎈ Ctrl⎇ Alt⇧ ShiftS the extruded section. Also note that the shear tool always uses the viewport axis, so switch to front or side view to keep the movement in line with your object.
You could also extrude past the point you want and use the knife or bisect tool to cut the geometry at the angle you want.
I found the answer. This doesn't need complex techniques. I just did
Extrude > Merge > At the First.
That's it. Now I got the shape I wanted.

How to detect an image between shapes from camera

I've been searching around the web about how to do this and I know that it needs to be done with OpenCV. The problem is that all the tutorials and examples that I find are for separated shapes detection or template matching.
What I need is a way to detect the contents between 3 circles (which can be a photo or something else). From what I searched, its not to difficult to find the circles with the camera using contours but, how do I extract what is between them? The circles work like a pattern on the image to grab what is "inside the pattern".
Do I need to use the contours of each circle and measure the distance between them to grab my contents? If so, what if the image is a bit rotated/distorted on the camera?
I'm using Xamarin.iOS for this but from what I already saw, I believe I need to go native for this and any Objective C example is welcome too.
EDIT
Imagining that the image captured by the camera is this:
What I want is to match the 3 circles and get the following part of the image as result:
Since the images come from the camera, they can be rotated or scaled up/down.
The warpAffine function will let you map the desired area of the source image to a destination image, performing cropping, rotation and scaling in a single go.
Talking about rotation and scaling seem to indicate that you want to extract a rectangle of a given aspect ratio, hence perform a similarity transform. To define such a transform, three points are too much, two suffice. The construction of the affine matrix is a little tricky.

How does Blender calculate vertex normals?

I'm attempting to calculate vertex normals for various game assets. The normals I calculate are used for "inflating" the model (to draw behind the real model producing a thick outline).
I currently compute the normal for each face and average all of them (several other questions on Stack Overflow suggest this approach). However, this doesn't work for sharp corners like this one (adjacent faces' normals marked in orange, the normal I'm trying to calculate is outlined in green).
The object looks like a small pedestal and we're looking at the front-left corner. There are three adjoining faces (the bottom face isn't visible; its normal points straight down).
Blender computes an excellent normal that lies squarely in the middle of the three faces' normals; it seems like it somehow calculates a normal that has minimum rotation to each of the three face normals. Blender's normal also doesn't change when the quads are triangulated differently.
Averaging the faces' normals gives me a different normal that points slightly upward in the Z-axis (-0.45, -0.89, +0.08). Inflating my model this way doesn't produce a good outline because the bottom face of the outline is shifted up and doesn't enclose the original model.
I attempted to look at the Blender source code but couldn't find what I was looking for. If anyone can point me to the algorithm in the Blender source, I'd accept that also.
Weight the surface normals by the angle of the faces where they join. It is a common practice in surface rendering (see discussion here: http://www.bytehazard.com/code/vertnorm.html), and will ensure that your bottom face is weighted stronger than the two slanted side faces. I don't know if Blender does it differently, but you should give it a try.

Is it possible to animate markers in ArcMap?

I'm completely new to ArcGIS and ArcMap, but someone suggested this program to me for a project I'm working on.
I would like to animate individual entities on a map, and was wondering if it is possible to do so in ArcMap. I asked this earlier here and a member directed me to a tutorial on animating in ArcGIS. The animation in the guide was over a map spread (ie. each pixel on the map displays, say, a different color to indicate population data in the area). However I realized that if I zoom in a lot, eventually the image will degenerate into pixels, which is why I need an actual object to mark a certain point. I checked some online tutorials and it seems like we can place markers on the map. Can someone tell me if it is possible to animate these markers (for example via a for-loop)? And if so, could you point me in a direction where to start?
Thanks in advance!
You can animate layers in ArcMap is the short answer. Its not as simple as using the timeline feature in Google Earth for example though. But then ArcMap is much more than just a visualization tool.
This help page on the ESRI web help looks like a good place to start.
I'm not 100% sure what you mean by the image degenerates into pixels. Are you saying that the markers were single points in the layer. Unlike Google Earth you are not confined to simply plotting points on the map. You can draw completely arbitrary shapes in ArcMap, which can be defined to cover actual areas of the map, so when you zoom-in the shape gets larger.
The way you need to load data into ArcMap to produce an animation isn't too simple. There might be other ways to do this, but the way I know of is to generate a NetCDF file. This file contains a 3D matrix of layer data, where each layer is separated through time. Because you generate a matrix, you are effectively placing a raster image over the map. Thus if you want to cover a large area, each matrix becomes large, and you multiply that by the number of time slices you wish to animate over.
Once you have a NetCDF file with your data in however, getting ArcMap to animate it and produce say a .avi file is pretty simple.
You could try just loading some of the example NetCDF datasets into ArcMap to see how/if they will work to get you started.
Hope that helps.
The upcoming v10 will have better time-aware capabilities, which will allow for animation.