How is this ray casting algorithm flawed? - algorithm

Matrix operations performed on the GPU can be pretty hard to debug because GPU operations don't really allow for console logs.
I've written one designed for a real time 2D rendering engine based on a very simple form of I guess what could be called ray casting and am having trouble figuring out what's wrong with it (it's outputting [0,0,0,255,0,0,0,255,...] instead of populating colors).
this.thread.x is the index of the current unit (color channel) in the matrix being operated on.
scene is a buffer made up of 6-unit clumps, each value containing, in order:
The type of entity, always 1 for "sprite" in this case.
The sprite ID, corresponding the the index in this.constants.textures containing the buffer for the entity's sprite.
X offset, the left edge of the sprite
Y offset, the top edge of the sprite
width of the sprite
height of the sprite
bufferWidth is the width of the render area multiplied by 4 channels.
this.constants.textures is an array containing buffers of each sprite which the sprite IDs from the scene refer to.
Note: For those curious, this is being done with GPU.js, a JavaScript lib that converts a JS func into GLSL code to be run via WebGL.
function(scene, sceneLength, bufferWidth) {
var channel = this.thread.x % 4;
if (channel === 3) {
return 255;
}
var x = this.thread.x % bufferWidth;
var y = Math.floor(this.thread.x / bufferWidth);
for (let i1 = 0; i1 < sceneLength; i1 += 6) {
var id = scene[i1 + 1];
var x1 = scene[i1 + 2];
var y1 = scene[i1 + 3];
var w1 = scene[i1 + 4];
var h1 = scene[i1 + 5];
var r1 = scene[i1 + 6];
var offsetX1 = x1 - x;
if (offsetX1 > 0 && offsetX1 < w1) {
var offsetY1 = y1 - y;
if (offsetY1 > 0 && offsetY1 < h1) {
var c1 = offsetY1 * w1 * 4 + offsetX1 * 4;
var c1R = c1 - (c1 % 4);
var c1A = c1R + 3;
if (this.constants.textures[id][c1A] != 0) {
return this.constants.textures[id][c1];
}
}
}
}
return 0;
}
Explanation for the concept I'm trying to implement:
With a matrix operation, when you want to draw a sprite if you were to perform a pass on the entire render area, you'd be doing far more work than necessary. If you break the rendering area down into chunks and only update the sections involved in the sprite being drawn, that would be a fairly decent way to do it. It would certainly be good enough for real time game rendering. This would be a multi-pass approach, where sprites are rendered one at a time.
Alternatively, for what seems to me to be the most optimal approach possible, instead of that, we can use a single-pass approach that performs a single matrix operation for the entire rendering area, evaluating for each color channel what should be there based on doing a very basic form of collision detection with each sprite in the scene and the relevant pixel in that sprite.

You're calculating your sprite offsets backwards, the calculations should be:
var offsetX1 = x - x1;
and
var offsetY1 = y - y1;
The offsets should increase as x and y increase (assuming the sprite co-ordinates have the same co-ordinate system as the screen co-ordinates), so you shouldn't be subtracting x and y.

Related

Shape appears to have less vertexes than shape data THREE.JS

I'm trying to create a smooth "wave" when the mouse moves over isometric logo shape.
I've created in in processing now I'm trying to recreate it in THREE.js
The shape acts strangely - the shape doesn't look as smooth when elevated compared to the processing sketch. If you look at the edges you can see segments that are not supposed to be there. I'm not sure what causes this.
Basically the shape is created through a loops that goes over 2 arrays:
for (var i = 0; i < xpos0.length; i++) {
shape.lineTo(xpos0[i], ypos0[i]);
}
Then it animates through another for loop that checks the distance between verteces[i].x and mouse location intersection with the ground
for (let p = 0; p < mesh.geometry.vertices.length; p=p+1) {
let delta = Math.abs(mesh.geometry.vertices[p].x - intersects[0].point.x);
mesh.geometry.vertices[p].z = bump2(-2, 2000, -1, 2, delta);
}
z value is calculated through this function:
function bump2(a,b,c,d,xval) {
xval = parseFloat(xval);
// console.log(typeof xval);
return Math.exp(a / (-xval * xval / b + c) + d) * -1;
}
https://codepen.io/NotYetDesignLab/pen/JjYaqRJ
How it looks on THREE.JS
notice how some segments appear "broken", like it's made of stiff parts instead of the many points that make up the segment in the array and give the illusion of "paper".
THIS IS HOW IT'S SUPPOSED TO LOOK: (Processing/java)
This has been done using Processing. Notice how the elevation of the edges is smooth and not broken.

Processing - creating circles from current pixels

I'm using processing, and I'm trying to create a circle from the pixels i have on my display.
I managed to pull the pixels on screen and create a growing circle from them.
However i'm looking for something much more sophisticated, I want to make it seem as if the pixels on the display are moving from their current location and forming a turning circle or something like this.
This is what i have for now:
int c = 0;
int radius = 30;
allPixels = removeBlackP();
void draw {
loadPixels();
for (int alpha = 0; alpha < 360; alpha++)
{
float xf = 350 + radius*cos(alpha);
float yf = 350 + radius*sin(alpha);
int x = (int) xf;
int y = (int) yf;
if (radius > 200) {radius =30;break;}
if (c> allPixels.length) {c= 0;}
pixels[y*700 +x] = allPixels[c];
updatePixels();
}
radius++;
c++;
}
the function removeBlackP return an array with all the pixels except for the black ones.
This code works for me. There is an issue that the circle only has the numbers as int so it seems like some pixels inside the circle won't fill, i can live with that. I'm looking for something a bit more complex like I explained.
Thanks!
Fill all pixels of scanlines belonging to the circle. Using this approach, you will paint all places inside the circle. For every line calculate start coordinate (end one is symmetric). Pseudocode:
for y = center_y - radius; y <= center_y + radius; y++
dx = Sqrt(radius * radius - y * y)
for x = center_x - dx; x <= center_x + dx; x++
fill a[y, x]
When you find places for all pixels, you can make correlation between initial pixels places and calculated ones and move them step-by-step.
For example, if initial coordinates relative to center point for k-th pixel are (x0, y0) and final coordinates are (x1,y1), and you want to make M steps, moving pixel by spiral, calculate intermediate coordinates:
calc values once:
r0 = Sqrt(x0*x0 + y0*y0) //Math.Hypot if available
r1 = Sqrt(x1*x1 + y1*y1)
fi0 = Math.Atan2(y0, x0)
fi1 = Math.Atan2(y1, x1)
if fi1 < fi0 then
fi1 = fi1 + 2 * Pi;
for i = 1; i <=M ; i++
x = (r0 + i / M * (r1 - r0)) * Cos(fi0 + i / M * (fi1 - fi0))
y = (r0 + i / M * (r1 - r0)) * Sin(fi0 + i / M * (fi1 - fi0))
shift by center coordinates
The way you go about drawing circles in Processing looks a little convoluted.
The simplest way is to use the ellipse() function, no pixels involved though:
If you do need to draw an ellipse and use pixels, you can make use of PGraphics which is similar to using a separate buffer/"layer" to draw into using Processing drawing commands but it also has pixels[] you can access.
Let's say you want to draw a low-res pixel circle circle, you can create a small PGraphics, disable smoothing, draw the circle, then render the circle at a higher resolution. The only catch is these drawing commands must be placed within beginDraw()/endDraw() calls:
PGraphics buffer;
void setup(){
//disable sketch's aliasing
noSmooth();
buffer = createGraphics(25,25);
buffer.beginDraw();
//disable buffer's aliasing
buffer.noSmooth();
buffer.noFill();
buffer.stroke(255);
buffer.endDraw();
}
void draw(){
background(255);
//draw small circle
float circleSize = map(sin(frameCount * .01),-1.0,1.0,0.0,20.0);
buffer.beginDraw();
buffer.background(0);
buffer.ellipse(buffer.width / 2,buffer.height / 2, circleSize,circleSize);
buffer.endDraw();
//render small circle at higher resolution (blocky - no aliasing)
image(buffer,0,0,width,height);
}
If you want to manually draw a circle using pixels[] you are on the right using the polar to cartesian conversion formula (x = cos(angle) * radius, y = sin(angle) * radius).Even though it's focusing on drawing a radial gradient, you can find an example of drawing a circle(a lot actually) using pixels in this answer

how to figure out cursive paths for an enemy to follow

The Problem
I am making a game where enemies appear at some point on the screen then follow a smooth curvy path and disappear at some point. I can make them follow a straight path but can't figure out the way to make them follow the paths depicted in the image.
Attempts
I started with parabolic curve and implemented them successfully. I just used the equation of parabola to calculate the coordinates gradually. I have no clue what is the equation for desired paths supposed to be.
What I want
I am not asking for the code.I just want someone to explain me the general technique.If you still want to show some code then I don't have special preference for programming language for this particular question you can use C,Java or even pseudo-code.
First you need to represent each curve with a set of points over time, For example:
-At T(0) the object should be at (X0, Y0).
-At T(1) the object should be at (X1, Y1).
And the more points you have, the more smooth curve you will get.
Then you will use those set of points to generate two formulas-one for X, and another one for Y-, using any Interpolation method, like The La-grange's Interpolation Formula:
Note that you should replace 'y' with the time T, and replace 'x' with your X for X formula, and Y for Y formula.
I know you hoped for a simple equation, but unfortunately this is will take from you a huge effort to simplify each equation, and my advise DON'T do it unless it's worth it.
If you are seeking for a more simple equation to perform well in each frame in your game you should read about SPline method, In this method is about splitting your curve into a smaller segments, and make a simple equation for every segment, for example:
Linear Spline:
Every segment contains 2 points, this will draw a line between every two points.
The result will be some thing like this:
Or you could use quadratic spline, or cubic spline for more smooth curves, but it will slow your game performance. You can read more about those methods here.
I think linear spline will be great for you with reasonable set of points for each curve.
Please change the question title to be more generic.
If you want to generate a spiral path you need.
Total time
How many full rotations
Largest radius
So, total time T_f = 5sec, rotations R_f = 2.5 * 2 * PI, the final distance from the start D_f = 200px
function SpiralEnemy(spawnX, spawnY, time) {
this.startX = spawnX;
this.startY = spawnY;
this.startTime = time;
// these will change and be used for rendering
this.x = this.startX;
this.y = this.startY;
this.done = false;
// constants we figured out above
var TFinal = 5.0;
var RFinal = -2.6 * 2 * Math.PI;
var RStart = -Math.PI / 2;
var DFinal = 100;
// the update function called every animation tick with the current time
this.update = function(t) {
var delta = t - this.startTime;
if(delta > TFinal) {
this.done = true;
return;
}
// find out how far along you are in the animation
var percent = delta / TFinal;
// what is your current angle of rotation (in radians)
var angle = RStart + RFinal * percent;
// how far from your start point should you be
var dist = DFinal * percent;
// update your coordinates
this.x = this.startX + Math.cos(angle) * dist;
this.y = this.startY + Math.sin(angle) * dist;
};
}
EDIT Here's a jsfiddle to mess with http://jsfiddle.net/pxb3824z/
EDIT 2 Here's a loop (instead of spiral) version http://jsfiddle.net/dpbLxuz7/
The loop code splits the animation into 2 parts the beginning half and the end half.
Beginning half : angle = Math.tan(T_percent) * 2 and dist = Speed + Speed * (1 - T_percent)
End half : angle = -Math.tan(1 - T_percent) * 2 and dist = **Speed + Speed * T_percent
T_percent is normalized to (0, 1.0) for both halfs.
function LoopEnemy(spawnX, spawnY, time) {
this.startX = spawnX;
this.startY = spawnY;
this.startTime = time;
// these will change and be used for rendering
this.x = this.startX;
this.y = this.startY;
this.last = time;
this.done = false;
// constants we figured out above
var TFinal = 5.0;
var RFinal = -2 * Math.PI;
var RStart = 0;
var Speed = 50; // px per second
// the update function called every animation tick with the current time
this.update = function(t) {
var delta = t - this.startTime;
if(delta > TFinal) {
this.done = true;
return;
}
// find out how far along you are in the animation
var percent = delta / TFinal;
var localDelta = t - this.last;
// what is your current angle of rotation (in radians)
var angle = RStart;
var dist = Speed * localDelta;
if(percent <= 0.5) {
percent = percent / 0.5;
angle -= Math.tan(percent) * 2;
dist += dist * (1 - percent);
} else {
percent = (percent - 0.5) / 0.5;
angle -= -Math.tan(1 - percent) * 2;
dist += dist * percent;
}
// update your coordinates
this.last = t;
this.x = this.x + Math.cos(angle) * dist;
this.y = this.y + Math.sin(angle) * dist;
};
}
Deriving the exact distance traveled and the height of the loop for this one is a bit more work. I arbitrarily chose a Speed of 50px / sec, which give a final x offset of ~+145 and a loop height of ~+114 the distance and height will scale from those values linearly (ex: Speed=25 will have final x at ~73 and loop height of ~57)
I don't understand how you give a curve. If you need a curve depicted on the picture, you can find a curve is given analytically and use it. If you have not any curves you can send me here: hedgehogues#bk.ru and I will help find you. I leave e-mail here because I don't get any messages about answers of users from stackoverflow. I don't know why.
If you have some curves in parametric view in [A, B], you can write a code like this:
struct
{
double x, y;
}SPoint;
coord = A;
step = 0.001
eps = 1e-6;
while (coord + step - eps < B)
{
SPoint p1, p2;
p1.x = x(coord);
p1.y = y(coord);
coord += step;
p2.x = x(coord);
p2.y = y(coord);
drawline(p1, p2);
}

Calculate the vertex while creating terrain from heightmap using ThreeJs

I'm reading "create terrain from heightmap" example from ThreeJs Cookbook
This example load GrandCanyon: http://lh5.ggpht.com/_-B0hFoGrn-w/SvHiYk39yAI/AAAAAAAABOQ/6IGZwifUYGA/GrandCanyon.png
And create a 3D terrain: http://www.smartjava.org/tjscb/02-geometries-meshes/02.06-create-terrain-from-heightmap.html
There are some code pieces I can not understand:
// draw on canvas
ctx.drawImage(img, 0, 0);
var pixel = ctx.getImageData(0, 0, width, depth);
var geom = new THREE.Geometry;
var output = [];
for (var x = 0; x < depth; x++) {
for (var z = 0; z < width; z++) {
// get pixel
// since we're grayscale, we only need one element
var yValue = pixel.data[z * 4 + (depth * x * 4)] / heightOffset;
var vertex = new THREE.Vector3(x * spacingX, yValue, z * spacingZ);
geom.vertices.push(vertex);
}
}
why is yValue calculated with that value ? why don't we use var yValue = pixel.data[z * 4 + (depth * x )] or something like that ?
And do we really need spacingX and spacingZ ?
Source code is here: https://github.com/josdirksen/threejs-cookbook/blob/master/02-geometries-meshes/02.06-create-terrain-from-heightmap.html
Could you please help me ?
Thank you very much!
You don't NEED spacingX and spacingZ, no. You could adjust scale in other ways, like applying a scale matrix to the entire THREE.Geometry after you've populated the vertices. Up to you, really.
As fort the yValue, the indexing is to adjust for the way the data for the texture is laid out. There are four channels, usually RGBA, but in this case we only need one of them as a height.

Fast algorithm for image distortion

I am working on a tool which distorts images, the purpose of the distortion is to project images to a sphere screen. The desired output is as the following image.
The code I use is as follow - for every Point(x, y) in the destination area, I calculate the corresponding pixel (sourceX, sourceY) in the original image to retrieve from.
But this approach is awkwardly slow, in my test, processing the sunset.jpg (800*600) requires more than 1500ms, if I remove the Mathematical/Trigonometrical calculations, calling cvGet2D and cvSet2D alone require more than 1200ms.
Is there a better way to do this? I am using Emgu CV (a .NET wrapper library for OpenCV) but examples in other language is also OK.
private static void DistortSingleImage()
{
System.Diagnostics.Stopwatch stopWatch = System.Diagnostics.Stopwatch.StartNew();
using (Image<Bgr, Byte> origImage = new Image<Bgr, Byte>("sunset.jpg"))
{
int frameH = origImage.Height;
using (Image<Bgr, Byte> distortImage = new Image<Bgr, Byte>(2 * frameH, 2 * frameH))
{
MCvScalar pixel;
for (int x = 0; x < 2 * frameH; x++)
{
for (int y = 0; y < 2 * frameH; y++)
{
if (x == frameH && y == frameH) continue;
int x1 = x - frameH;
int y1 = y - frameH;
if (x1 * x1 + y1 * y1 < frameH * frameH)
{
double radius = Math.Sqrt(x1 * x1 + y1 * y1);
double theta = Math.Acos(x1 / radius);
int sourceX = (int)(theta * (origImage.Width - 1) / Math.PI);
int sourceY = (int)radius;
pixel = CvInvoke.cvGet2D(origImage.Ptr, sourceY, sourceX);
CvInvoke.cvSet2D(distortImage, y, x, pixel);
}
}
}
distortImage.Save("Distort.jpg");
}
Console.WriteLine(stopWatch.ElapsedMilliseconds);
}
}
From my personal experience, I was doing some stereoscopic vision stuff, the best way to talk to openCV is through own wrapper, you could put your method in c++ and call it from c#, that would give you 1 call to native, faster code, and because under the hood Emgu's keeping OpenCV data, it's also possible to create an image with emgu, process it natively and enjoy processed image in c# again.
The get/set methods looks like Gdi's GetPixel / SetPixel ones, and, according to documentation they are "slow but safe way".
For staying with Emgu only, documentation tells that if you want to iterate over pixels, you should access .Data property:
The safe (slow) way
Suppose you are working on an Image. You can obtain the pixel on the y-th row and x-th column by calling
Bgr color = img[y, x];
Setting the pixel on the y-th row and x-th column is also simple
img[y,x] = color;
The fast way
The Image pixels values are stored in the Data property, a 3D array. Use this property if you need to iterate through the pixel values of the image.

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