I'm making a top-down shooter and the player's gun is offset from the coordinates of the object. I'm using GameMaker:Studio, so the x and y coords are the center of the object. The offset of the image is set here:
bullet_offset_x = 30;
bullet_offset_y = 28;
And here is the code for shooting the gun:
var xpos = x + (bullet_offset_x * cos(degtorad(direction))) - (bullet_offset_y * sin(degtorad(direction)));
var ypos = y + (bullet_offset_x * sin(degtorad(direction))) + (bullet_offset_y * cos(degtorad(direction)));
var flash = instance_create(xpos, ypos, obj_flash);
with (flash){
direction = other.direction;
image_angle = other.direction;
}
I'm using the following formula for placing the muzzle flash:
x' = xcos(angle) - ysin(angle)
y' = xsin(angle) + ycos(angle)
Therefore:
xpos = x + x' and ypos = x + y'
However, when I run the code, the muzzle flash is correctly positioned when the angle is 0/360, but is off otherwise. Am I calculating this wrong?
IMAGES:
Correct
Incorrect
You need to use lengthdir_x and lengthdir_y functions, like:
var xpos = x + lengthdir_x(offset_distance, offset_angle + image_angle); // or direction
var ypos = y + lengthdir_y(offset_distance, offset_angle + image_angle);
var flash = instance_create(xpos, ypos, obj_flash);
flash.direction = direction;
flash.image_angle = direction;
little example here
To calculate the values to be substituted into the formula, you can use this program.
Originally it was made in Russian, but I have translated it into English. My English is terrible, but I hope you will be able to understand it.
upd: Example with offsets:
var delta_x = 60;
var delta_y = -70;
var angle = point_direction(0, 0, delta_x, delta_y);
var distance = point_distance(0, 0, delta_x, delta_y);
var xpos = x + lengthdir_x(distance, image_angle + angle);
var ypos = y + lengthdir_y(distance, image_angle + angle);
var obj = instance_create(xpos, ypos, obj_flash);
obj.image_angle = image_angle;
When your sprite has an angle of 0, your muzzle flash still at an angle of invtan(28/30) in relation to the sprite. Therefore, the angle that the flash must be placed at in relation to the rotation of the sprite can be given by
flashRotation = spriteRotationDegrees - invtan(28/30) \\you can change this to radians
Once that is found, the positions can be found by:
var x_pos = sprite_x_pos + Math.Sqrt(28^2 + 30^2)cos(flashRotation);
var y_pos = sprite_y_pos + Math.Sqrt(28^2 + 30^2)sin(flashRotation);
The actual angle of rotation of the flash (which way it points) will be the same angle as the sprite.
You may need to play with the flashRotaion equation depending upon which way is counted as a positive rotation.
Related
I would like to make a simple animation of the character rotating itself when it jumps. I'm making an indie platformer so this should be simple to do, I think, but I'm too newbie for this.
Here's the movement code.
//------------------------- MOVEMENT INPUT
xMove = kRight - kLeft;
xSpd = xMove * mSpd;
ySpd += 0.65;
//------------------------- JUMP
onGround = place_meeting(x,y+1,oSolid);
if(onGround) airJump = 1;
if(kJump){
if(onGround or airJump > 0){
ySpd = -12;
airJump = 0;
}
}
//------------------------- FINAL MOVEMENT
if(place_meeting(x + xSpd, y, oSolid)){
while(!place_meeting(x + sign(xSpd), y, oSolid)) x += sign(xSpd);
xSpd = 0;
}
if(place_meeting(x + xSpd, y + ySpd, oSolid)){
while(!place_meeting(x + xSpd, y + sign(ySpd), oSolid)) y += sign(ySpd);
ySpd = 0;
}
x += xSpd;
y += ySpd;
if xSpd < 0 dir = -1;
if xSpd > 0 dir = 1;
The player is a simple square, so I would like to make it rotate 360 degrees while on the air.
You should be able to use image_angle for this, changing the value will change the angle of the sprite, and continiously increasing/decreasing that value will simulate a rotation.
However, keep in mind that if you rotate the sprite, the hitbox of the sprite will rotate as well. You can probably set the hitbox apart from the sprite so it won't interrupt with each other.
Example:
https://manual.yoyogames.com/GameMaker_Language/GML_Reference/Asset_Management/Sprites/Sprite_Instance_Variables/image_angle.htm
For player movement collision handling you want to avoid using image_angle variable by using your own variable for the image rotation with the draw_sprite_ext function. Also by change you end up wanting to use the image angle for anything its good to wrap it mostly later if your trying to use fov and what not.
For example
function Scr_Player_Create(){
image_offset = 0;
}
function Scr_Player_Step(){
image_offset += (keyboard_check(vk_right) - keyboard_check(vk_left)) * 10;
image_offset = wrap(image_offset, 0, 359);
}
function Scr_Player_Draw(){
draw_sprite_ext( sprite_index, image_index, x, y, image_xscale, image_yscale,
image_angle + image_offset, image_blend, image_alpha );
draw_text(10, 10, image_offset);
}
function wrap(wrap_value, wrap_minimum, wrap_maximum){
// Credit: Juju from GMLscripts forums!
var _mod = ( wrap_value - wrap_minimum ) mod ( wrap_maximum - wrap_minimum );
if ( _mod < 0 ) return _mod + wrap_maximum else return _mod + wrap_minimum;
}
Another approach you could do to avoid image_angle effecting your collision is this
var _angle = image_angle;
image_angle += image_offset;
draw_self();
image_angle = _angle;
I know Rectangle is axis aligned, that's fine, I just can't figure out how to create a rectangle so it is always encompassing the entire sprite, regardless of rotation. I have been looking everywhere for an answer but I can't get a straight one anywhere.
For example:
Assuming the origin point is the middle of the texture, how can I go about this?
EDIT
Fiddling around with it a little, I've gotten this far:
public Rectangle BoundingBox
{
get
{
var cos = Math.Cos(SpriteAngle);
var sin = Math.Cos(SpriteAngle);
var t1_opp = Width * cos;
var t1_adj = Math.Sqrt(Math.Pow(Width, 2) - Math.Pow(t1_opp, 2));
var t2_opp = Height * sin;
var t2_adj = Math.Sqrt(Math.Pow(Height, 2) - Math.Pow(t2_opp, 2));
int w = Math.Abs((int)(t1_opp + t2_opp));
int h = Math.Abs((int)(t1_adj + t2_adj));
int x = Math.Abs((int)(Position.X) - (w / 2));
int y = Math.Abs((int)(Position.Y) - (h / 2));
return new Rectangle(x, y, w, h);
}
}
(doing this off the top of my head.. but the principle should work)
Create a matrix to rotate around the center of the rectangle - that is a translate of -(x+width/2), -(y+height/2)
followed by a rotation of angle
followed by a translate of (x+width/2), (y+height/2)
Use Vector2.Transform to transform each corner of the original rectangle
Then make a new rectangle with
x = min(p1.x, p2.x, p3.x, p4.x)
width = max(p1.x, p2.x, p3.x, p4.x) - x
similar for y
Sorry this is coming so late, but I figured this out a while ago and forgot to post an answer.
public virtual Rectangle BoundingBox
{
get
{
int x, y, w, h;
if (Angle != 0)
{
var cos = Math.Abs(Math.Cos(Angle));
var sin = Math.Abs(Math.Sin(Angle));
var t1_opp = Width * cos;
var t1_adj = Math.Sqrt(Math.Pow(Width, 2) - Math.Pow(t1_opp, 2));
var t2_opp = Height * sin;
var t2_adj = Math.Sqrt(Math.Pow(Height, 2) - Math.Pow(t2_opp, 2));
w = (int)(t1_opp + t2_opp);
h = (int)(t1_adj + t2_adj);
x = (int)(Position.X - (w / 2));
y = (int)(Position.Y - (h / 2));
}
else
{
x = (int)Position.X;
y = (int)Position.Y;
w = Width;
h = Height;
}
return new Rectangle(x, y, w, h);
}
}
This is it here. In my work in the edit, I accidentally had Math.Cos in the sin variable, which didn't help.
So it's just basic trigonometry. If the textures angle is something other than zero, calculate the sides of the two triangles formed by the width and the height, and use the sides as the values for the width and the height, then center the rectangle around the texture. If that makes sense.
Here's a picture to help explain:
Here's a gif of the final result:
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);
}
I'm struggling with some quaternion code in iOS. I have an open cube, which i've rotated into an isometric view. i am able to rotate the cube with touch and rotate about its axis and also zoom in/out. I also have labels associated with the cube - which also need to rotate with the cube. Again, i've managed to do this.
However, i'm now trying to implement being able to drag the label (ie. translate it) from one position, to another. If we look at the image below, what i've tried to illustrate is that i want to be able to translate the label from "label from" to the position "label to". Then, when i come to rotating the cube, the label should stay in its new position and rotate with the cube. However, i'm making a cock-up of this translation and when i try rotating the cube, the label jumps to a new position since i've not set the label coordinates properly.
I have the quaternion associated with the cube.
With the following code, i have been able to translate the label properly when the quaternion is set to [0, 0, 0, 1] (so that the cube is front-on - looks like a square from this position).
- (void) rotateWithAngle:(float) radians andVector:(GLKVector3) axis andScale:(float) scale
{
if (radians != self.lastRadians
|| (axis.v[0] != self.lastAxis.v[0] || axis.v[1] != self.lastAxis.v[1] || axis.v[2] != self.lastAxis.v[2])
|| scale != self.lastScale)
{
GLKMatrix4 m = GLKMatrix4MakeTranslation(self.normX, self.normY, self.normZ);
if (radians != 0)
m = GLKMatrix4Rotate(m, radians, axis.x, -axis.y, axis.z);
m = GLKMatrix4Scale(m, scale, scale, scale);
float x = (m.m00 * m.m30) + (m.m01 * m.m31) + (m.m02 * m.m32) + (m.m03 * m.m33);
float y = (m.m10 * m.m30) + (m.m11 * m.m31) + (m.m12 * m.m32) + (m.m13 * m.m33);
float z = (m.m20 * m.m30) + (m.m21 * m.m31) + (m.m22 * m.m32) + (m.m23 * m.m33);
x /= m.m33;
y /= m.m33;
z /= m.m33;
float w = (((x+self.winSz) / (self.winSz * 2.0)) * self.parentFrame.size.width) + self.parentFrame.origin.x;
float h = (((y+self.winSz) / (self.winSz * 2.0)) * self.parentFrame.size.height) + self.parentFrame.origin.y;
self.lastRadians = radians;
self.lastAxis = axis;
self.lastScale = scale;
[self setCenter:CGPointMake(w,h)];
}
}
- (void) translateFromTouch:(UIPanGestureRecognizer *) pan
{
CGPoint translation = [pan translationInView:self];
CGPoint imageViewPosition = self.center;
GLKVector3 axis = GLKQuaternionAxis(*_quaternion);
float rot = GLKQuaternionAngle(*_quaternion);
CGFloat h = self.parentFrame.size.height;
CGFloat w = self.parentFrame.size.width;
imageViewPosition.x += translation.x;
imageViewPosition.y += translation.y;
self.center = imageViewPosition;
// recalculate the norm position
float x = ((2.0 * self.winSz * (imageViewPosition.x - self.parentFrame.origin.x)) / w) - self.winSz;
float y = ((2.0 * self.winSz * (imageViewPosition.y - self.parentFrame.origin.y)) / h) - self.winSz;
self.normX = x;
self.normY = y;
[pan setTranslation:CGPointZero inView:self];
}
These methods are hit if a label (based on a UILabel) is either dragged or the cube (or the opengl scene) is rotated.
This works when we are looking front-on, so that the x,y values can easily be converted from pixel coords into normal or world coords.
However, when the axis is not front-on, i'm struggling to figure it out. For instance, we we have the quaternion set at (0, sqrt(2)/2, 0, sqrt(2)/2) then all x translations correspond to z world coords. So how do i make this connection/calculation? I'm sure it's fairly easy but i've hit a wall with this.
(winSz i have set to 1.5. model coords very between -1 and 1)
I am trying to implement the collision detection between rotated rectangle and circle by following this http://www.migapro.com/circle-and-rotated-rectangle-collision-detection/
I have added the code in jsfiddle here http://jsfiddle.net/Z6KSX/2/.
What am i missing here ?
function check_coll ( circle_x,circle_y, rect_x, rect_y, rect_width, rect_height, rect_angle)
{
// Rotate circle's center point back
var rect_centerX = rect_x /2 ;
var rect_centerY = rect_y /2 ;
var cx = (Math.cos(rect_angle) * (circle_x - rect_centerX)) - (Math.sin(rect_angle) * (circle_y - rect_centerY)) + rect_centerX;
var cy = (Math.sin(rect_angle) * (circle_x - rect_centerX)) + (Math.cos(rect_angle) * (circle_y - rect_centerY)) + rect_centerY;
// Closest point
var x, y;
// Find the unrotated closest x point from center of unrotated circle
if (cx < rect_x) {
x = rect_x;
}
else if (cx > rect_x + rect_width){
x = rect_x + rect_width;
}
else{
x = cx;
}
// Find the unrotated closest y point from center of unrotated circle
if (cy < rect_y){
y = rect_y;
}
else if (cy > rect_y + rect_height) {
y = rect_y + rect_height;
}
else {
y = cy;
}
// Determine collision
var collision = false;
var c_radius = 5;
var distance = findDistance(cx, cy, x, y);
if (distance < c_radius) {
collision = true; // Collision
}
else {
collision = false;
}
return collision;
}
function findDistance (x1, y1, x2, y2) {
var a = Math.abs(x1 - x2);
var b = Math.abs(y1 - y2);
var c = Math.sqrt((a * a) + (b * b));
return c;
}
Hehe, I find this amusing as I somewhat recently solved this for myself after spending a large amount of time going down the wrong path.
Eventually I figured out a way:
1.) Simply rotate the point of the center of the circle by the Negative amount the rectangle has been rotated by. Now the point is 'aligned' with the rectangle (in the rectangles relative coordinate space).
2.) Solve for circle vs. AABB. The way I solved it gave me a point on the rectangle that is closest to the circle's center.
3.) Rotate the resulting point from by the Positive amount the rectangle has been rotated by. Continue solving as usual (checking if the distance between that point and the circle center is within the circle's radius)
From a very quick glance at your code, it seems like maybe you are doing the same thing, but missing the last step? I suggest drawing out your point on the rectangle from step 2 to see exactly where it is to help debug.
I was able to figure this out . The issue in the code was, I was using the wrong radius and had missed the center of rect_x and rect_y
var rect_centerX = rect_x + (rect_width / 2);
var rect_centerY = rect_y + (rect_height /2);
When dealing with rotation on the canvas we will need to add the translate values to the corresponding x and y values used in createrect.
I also use this code for my project and it's working. The only thing you need to do is use -angle instead of the angle.
Here is my code link
const canvas = document.getElementById("canvas");
const ctx = canvas.getContext("2d");
const rectX = 100;
const rectY = 100;
const rectWidth = 200;
const rectHeight = 100;
const circleRadius = 2;
const rectMidPointX = rectX + rectWidth / 2;
const rectMidPointY = rectY + rectHeight / 2;
const angle = Math.PI / 4;
let circleX;
let circleY;
canvas.addEventListener('mousemove', (e) => {
circleX = e.clientX;
circleY = e.clientY;
ctx.save();
ctx.beginPath();
ctx.fillStyle = '#fff';
ctx.arc(circleX, circleY, circleRadius, 0, 2 * Math.PI);
ctx.fill();
ctx.stroke();
ctx.restore();
calculateIntersection();
})
ctx.save();
//ctx.fillRect(100, 100, 100, 100);
ctx.strokeStyle = 'black';
ctx.translate(rectMidPointX, rectMidPointY);
ctx.rotate(angle);
ctx.translate(-rectMidPointX, -rectMidPointY);
ctx.strokeRect(rectX, rectY, rectWidth, rectHeight);
ctx.restore();
// Determine collision
let collision = false;
const findDistance = (fromX, fromY, toX, toY) => {
const a = Math.abs(fromX - toX);
const b = Math.abs(fromY - toY);
return Math.sqrt((a * a) + (b * b));
};
function calculateIntersection() {
// Rotate circle's center point back
const unrotatedCircleX = Math.cos(-angle) * (circleX - rectMidPointX) -
Math.sin(-angle) * (circleY - rectMidPointY) + rectMidPointX;
const unrotatedCircleY = Math.sin(-angle) * (circleX - rectMidPointX) +
Math.cos(-angle) * (circleY - rectMidPointY) + rectMidPointY;
// Closest point in the rectangle to the center of circle rotated backwards(unrotated)
let closestX, closestY;
// Find the unrotated closest x point from center of unrotated circle
if (unrotatedCircleX < rectX)
closestX = rectX;
else if (unrotatedCircleX > rectX + rectWidth)
closestX = rectX + rectWidth;
else
closestX = unrotatedCircleX;
// Find the unrotated closest y point from center of unrotated circle
if (unrotatedCircleY < rectY)
closestY = rectY;
else if (unrotatedCircleY > rectY + rectHeight)
closestY = rectY + rectHeight;
else
closestY = unrotatedCircleY;
const distance = findDistance(unrotatedCircleX, unrotatedCircleY, closestX, closestY);
if (distance < circleRadius)
collision = true; // Collision
else
collision = false;
console.log('collision', collision);
}
<canvas id="canvas" width="400px" height="400px" />