Develop Reference

How to use AffineTransform with very little coordinates?

I have a set of two dimensions points. Their X and Y are greater than -2 and lesser than 2. Such point could be : (-0.00012 ; 1.2334 ).
I would want to display these points on a graph, using rectangles (a rectangle illustrates a point, and has its coordinates set to its point's ones - moreover, it has a size of 10*10).
Rectangles like (... ; Y) should be displayed above any rectangles like (... ; Y-1) (positive Y direction is up). Thus, I must set the graph's origin not at the top-left hand-corner, but somewhere else.
I'm trying to use Graphics2D's AffineTransform to do that.
I get the minimal value for all the X coordinates
I get the minimal value for all the Y coordinates
I get the maximal value for all the X coordinates
I get the maximal value for all the Y coordinates
I get the distance xmax-xmin and ymax-ymin
Then, I wrote the code I give you below.
Screenshots
Some days ago, using my own method to scale, I had this graph:
(so as I explained, Y are inverted and that's not a good thing)
For the moment, i.e., with the code I give you below, I have only one point that takes all the graph's place! Not good at all.
I would want to have:
(without lines, and without graph's axis. The important here is that points are correctly displayed, according to their coordinates).
Code
To get min and max coordinates value:
x_min = Double.parseDouble((String) list_all_points.get(0).get(0));
x_max = Double.parseDouble((String) list_all_points.get(0).get(0));
y_min = Double.parseDouble((String) list_all_points.get(0).get(1));
y_max = Double.parseDouble((String) list_all_points.get(0).get(1));
for(StorableData s : list_all_points) {
if(Double.parseDouble((String) s.get(0)) < x_min) {
x_min = Double.parseDouble((String) s.get(0));
}
if(Double.parseDouble((String) s.get(0)) > x_max) {
x_max = Double.parseDouble((String) s.get(0));
}
if(Double.parseDouble((String) s.get(1)) < y_min) {
y_min = Double.parseDouble((String) s.get(1));
}
if(Double.parseDouble((String) s.get(1)) > y_max) {
y_max = Double.parseDouble((String) s.get(1));
}
}
To draw a point:
int x, y;
private void drawPoint(Cupple storable_data) {
//x = (int) (storable_data.getNumber(0) * scaling_coef + move_x);
//y = (int) (storable_data.getNumber(1) * scaling_coef + move_y);
x = storable_data.getNumber(0).intValue();
y = storable_data.getNumber(1).intValue();
graphics.fillRect(x, y, 10, 10);
graphics.drawString(storable_data.toString(), x - 5, y - 5);
}
To paint the graph:
#Override
public void paint(Graphics graphics) {
this.graphics = graphics;
Graphics2D graphics_2d = ((Graphics2D) this.graphics);
AffineTransform affine_transform = graphics_2d.getTransform();
affine_transform.scale(getWidth()/(x_max - x_min), getHeight()/(y_max - y_min));
affine_transform.translate(x_min, y_min);
graphics_2d.transform(affine_transform);
for(StorableData storable_data : list_all_points) {
graphics_2d.setColor(Color.WHITE);
this.drawPoint((Cupple) storable_data);
}

I suggest you map each data point to a point on the screen, thus avoiding the following coordinate system pitfalls. Take your list of points and create from them a list of points to draw. Take into account that:
The drawing is pixel-based, so you will want to scale your points (or you would have rectangles 1 to 4 pixels wide...).
You will need to translate all your points because negative values will be outside the boundaries of the component on which you draw.
The direction of the y axis is reversed in the drawing coordinates.
Once that is done, use the new list of points for the drawing and the initial one for calculations. Here is an example:
public class Graph extends JPanel {
private static int gridSize = 6;
private static int scale = 100;
private static int size = gridSize * scale;
private static int translate = size / 2;
private static int pointSize = 10;
List<Point> dataPoints, scaledPoints;
Graph() {
setBackground(Color.WHITE);
// points taken from your example
Point p1 = new Point(-1, -2);
Point p2 = new Point(-1, 0);
Point p3 = new Point(1, 0);
Point p4 = new Point(1, -2);
dataPoints = Arrays.asList(p1, p2, p3, p4);
scaledPoints = dataPoints.stream()
.map(p -> new Point(p.x * scale + translate, -p.y * scale + translate))
.collect(Collectors.toList());
}
#Override
public Dimension getPreferredSize() {
return new Dimension(size, size);
}
#Override
protected void paintComponent(Graphics g) {
super.paintComponent(g);
Graphics2D g2d = (Graphics2D) g;
// draw a grid
for (int i = 0; i < gridSize; i++) {
g2d.drawLine(i * scale, 0, i * scale, size);
g2d.drawLine(0, i * scale, size, i * scale);
}
// draw the rectangle
g2d.setPaint(Color.RED);
g2d.drawPolygon(scaledPoints.stream().mapToInt(p -> p.x).toArray(),
scaledPoints.stream().mapToInt(p -> p.y).toArray(),
scaledPoints.size());
// draw the points
g2d.setPaint(Color.BLUE);
// origin
g2d.fillRect(translate, translate, pointSize, pointSize);
g2d.drawString("(0, 0)", translate, translate);
// data
for (int i = 0; i < dataPoints.size(); i++) {
Point sp = scaledPoints.get(i);
Point dp = dataPoints.get(i);
g2d.fillRect(sp.x, sp.y, pointSize, pointSize);
g2d.drawString("(" + dp.x + ", " + dp.y + ")", sp.x, sp.y);
}
}
public static void main(String[] args) {
JFrame frame = new JFrame();
frame.setContentPane(new Graph());
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.pack();
frame.setLocationRelativeTo(null);
frame.setVisible(true);
}
}
And another:
You might want to have the points aligned on the grid intersections and not below and to the right of them. I trust you will figure this one out.
Also, I ordered the points so that drawPolygon will paint the lines in the correct order. If your points are arbitrarily arranged, look for ways to find the outline. If you want lines between all points like in your example, iterate over all combinations of them with drawLine.

Rotating PDFContentByte Overlay Content

I have created a watermark text that is vertically centered.
This is the line I used
PdfPatternPainter.showTextAlignedKerned(Element.ALIGN_MIDDLE,
string, x, y, -90);
What i want to do now is to make the watermark diagonal. changing the angle value will make it diagonal, but then its x,y position is not centered anymore.
this is my current method
public static void createWaterMarkPDF(ArrayList<String> watermark, PdfReader reader, PdfStamper stamper) throws Exception {
Rectangle pageSize = reader.getPageSize(1);
final float WATERMARK_PAGE_ANGLE = 270;
BaseFont font = BaseFont.createFont(BaseFont.HELVETICA, BaseFont.WINANSI, BaseFont.NOT_EMBEDDED);
PdfPatternPainter painter = stamper.getOverContent(1).createPattern(pageSize.getWidth(), pageSize.getHeight());
painter.setColorStroke(new BaseColor(192, 192, 192));
int FONT_SIZE = 80;
painter.beginText();
painter.setTextRenderingMode(PdfPatternPainter.TEXT_RENDER_MODE_FILL);
painter.setFontAndSize(font, FONT_SIZE);
for (int i=0; i<watermark.size(); i++) {
String string = watermark.get(i);
// Values are opposite since we are doing a vertical alignment angle
float width = font.getAscentPoint(string, FONT_SIZE) + font.getDescentPoint(string, FONT_SIZE);
float height = painter.getEffectiveStringWidth(string, true);
float x = (pageSize.getWidth() - width) / 2;
if (i == 0)
x += (width * 3);
else if (i == 2)
x -= (width * 3);
painter.showTextAlignedKerned(Element.ALIGN_MIDDLE,
string, x,
Util.transformY(pageSize, (pageSize.getHeight() - height) / 2),
WATERMARK_PAGE_ANGLE);
}
painter.endText();
// Transparency of watermark
PdfGState state = new PdfGState();
state.setFillOpacity(0.1f);
for (int i=reader.getNumberOfPages(); i>0; i--) {
Rectangle thisPageSize = reader.getPageSize(i);
PdfContentByte overContent = stamper.getOverContent(i);
overContent.setColorFill(new PatternColor(painter));
overContent.setGState(state);
overContent.rectangle(thisPageSize.getLeft(), thisPageSize.getBottom(), thisPageSize.getWidth(), thisPageSize.getHeight());
overContent.fill();
}
}
it draws vertical lines and centered. watermark is an ArrayList. you can add 3 strings.
if i change the angle to , say 300 (or -60) to make it diagonal, the positioning is whacked. do i need to use an AffineTransform here? although i already tried, didnt work for me unless i lacked something here?

Algorithm to verify if a shape is inside another - javafx

I have a rectangular and circle. I need to verify whether a rectangle is inside that circle.
I tried to Shape.intersects but intersects is checked the number 1.
Does anyone know this kind of algorithm in javafx?
Just to exemplifly, in the figure only rectangles 1, 2, 3, and 4 are inside the circle.
thanks for your help.

Solution
The basic idea behind this solution is that any polygon is contained within any convex (see comments) shape iff every point within the polygon is within the shape. The intersects() method that you're attempting to use returns true if at least one point of the polygon is within the shape. You've already figured out that it'll work, but it'll also offer false positives for any partially-intersected shapes. To fix it, we define our own intersection test which looks at all points.
This can be generalized to scan any given polygon for "total intersection" with any given shape:
public boolean totalIntersects(Polygon poly, Shape testShape) {
List<Point> points = flatDoublesToPoints(poly.getPoints());
boolean inside = true; // If this is false after testing all points, the poly has at least one point outside of the shape.
for(Point point : points) {
if(!testShape.intersects(point.x, point.y, 1, 1)) { // The 3rd and 4th parameters here are "width" and "height". 1 for a point.
inside = false;
}
}
return inside;
}
where flatDoublesToPoints() and Point are defined as:
private List<Point> flatDoublesToPoints(List<Double> flatDoubles) {
List<Point> points = new ArrayList<>();
for(int i = 0; i < flatDoubles.size(); i += 2) {
points.add(new Point(flatDoubles.get(i), flatDoubles.get(i + 1)));
}
return points;
}
class Point {
public double x, y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
}
flatDoublesToPoints() is needed to split the "flat" {x1, y1, x2, y2, x3, y3...} polygon lists into a more easy-to-understand data structure. If you're doing tons of comparisons, it may be helpful to skip this step, however, and operate on the "flat list" directly for memory reasons.
Application
The following applies the other methods to a situation extremely similar to yours. (Not exact, because I didn't have your code.)
public class Main extends Application {
public static final int SIZE = 600;
#Override
public void start(Stage primaryStage) throws Exception {
Pane rootPane = new Pane();
List<Rectangle> rects = new ArrayList<>();
for (int j = 0; j < 2; j++) {
for(int i = 0; i < 5; i++) {
Rectangle r = new Rectangle(i * 100, j == 0 ? 0 : 300, 100, 200);
r.setFill(Color.BEIGE);
r.setStroke(Color.BLACK);
rects.add(r);
}
}
rootPane.getChildren().addAll(rects);
Circle circle = new Circle(350, 100, 200);
circle.setStroke(Color.BLACK);
circle.setFill(null);
rootPane.getChildren().add(circle);
List<Polygon> polys = new ArrayList<>();
for(Rectangle rect : rects) {
polys.add(rectangleToPolygon(rect));
}
List<Polygon> intersects = getTotalIntersections(polys, circle);
System.out.println(intersects);
primaryStage.setScene(new Scene(rootPane, SIZE, SIZE));
primaryStage.show();
}
public List<Polygon> getTotalIntersections(List<Polygon> polys, Shape testShape) {
List<Polygon> intersections = new ArrayList<>();
for(Polygon poly : polys) {
if(totalIntersects(poly, testShape)) {
intersections.add(poly);
}
}
return intersections;
}
public static Polygon rectangleToPolygon(Rectangle rect) {
double[] points = {rect.getX(), rect.getY(),
rect.getX() + rect.getWidth(), rect.getY(),
rect.getX() + rect.getWidth(), rect.getY() + rect.getHeight(),
rect.getX(), rect.getY() + rect.getHeight()};
return new Polygon(points);
}
public static void main(String[] args) {
Main.launch(args);
}
}
This code will print the following:
[Polygon[points=[200.0, 0.0, 300.0, 0.0, 300.0, 200.0, 200.0, 200.0], fill=0x000000ff], Polygon[points=[300.0, 0.0, 400.0, 0.0, 400.0, 200.0, 300.0, 200.0], fill=0x000000ff], Polygon[points=[400.0, 0.0, 500.0, 0.0, 500.0, 200.0, 400.0, 200.0], fill=0x000000ff]]
Which is your three polygons labeled 2, 3, and 4.

I don't think that JavaFX will have some special methods for this case.
To draw that circle you need coordinates (X_c, Y_c) of center and radius (R).
To draw rectangles you need to have coordinates ((X_1, Y_1), (X_2, Y_2) etc.) of angle points.
Then all you need is to check if all points of the rectangle is inside of the circle:
(X_1 - X_c)^2 + (Y_1 - Y_c)^2 < R^2
(X_2 - X_c)^2 + (Y_2 - Y_c)^2 < R^2
...

Try this :
import javafx.geometry.Point2D;
import javafx.scene.shape.Circle;
import javafx.scene.shape.Rectangle;
/*
Check if a rectangle is contained with in a circle by checking
all rectangle corners.
For the rectangle to be contained in a circle, all its corners should be
in a distance smaller or equal to the circle's radius, from the circle's center.
Note:
Requires some more testing. I tested only a few test cases.
I am not familiar with javafx. This solution does not take into
calculation rectangle's arc or other attributes I may not be aware of.
*/
public class Test{
//apply
public static void main(String[] args){
Circle circle = new Circle(0 ,0, 100);
Rectangle rec = new Rectangle(0, 0, 50 , 50);
System.out.println("Is rectungle inside the circle ? "
+ isContained(circle,rec));
}
//check if rectangle is contained within a circle
private static boolean isContained(Circle circle,Rectangle rec) {
boolean isInside = true;
//get circle center & radius
Point2D center = new Point2D(circle.getCenterX(), circle.getCenterY());
double radius= circle.getRadius();
Point2D[] corners = getRectangleCorners(rec);
for(Point2D corner : corners) {
//if any corner falls outside the circle
//the rectangle is not contained in the circle
if(distanceBetween2Points(corner, center) > radius) {
return false;
}
}
return isInside;
}
//calculate distance between two points
//(updated a per fabian's suggestion)
private static double distanceBetween2Points
(Point2D corner, Point2D center) {
return corner.distance(center);
}
private static Point2D[] getRectangleCorners(Rectangle rec) {
Point2D[] corners = new Point2D[4];
corners[0] = new Point2D(rec.getX(), rec.getY());
corners[1] = new Point2D(rec.getX()+ rec.getWidth() , rec.getY());
corners[2] = new Point2D(rec.getX()+ rec.getWidth(), rec.getY()+ rec.getHeight());
corners[3] = new Point2D(rec.getX(), rec.getY()+ rec.getHeight());
return corners;
}
}

There is a working simple solution here : https://stackoverflow.com/a/8721483/1529139
Copy-paste here:
class Boundary {
private final Point[] points; // Points making up the boundary
...
/**
* Return true if the given point is contained inside the boundary.
* See: http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
* #param test The point to check
* #return true if the point is inside the boundary, false otherwise
*
*/
public boolean contains(Point test) {
int i;
int j;
boolean result = false;
for (i = 0, j = points.length - 1; i < points.length; j = i++) {
if ((points[i].y > test.y) != (points[j].y > test.y) &&
(test.x < (points[j].x - points[i].x) * (test.y - points[i].y) / (points[j].y-points[i].y) + points[i].x)) {
result = !result;
}
}
return result;
}
}

How to determine the coordinates of the next rectangle on JPanel

i have an arraylist RecArray of objects with each object containing two int values, one for the width and for the height of a rectangle. Each rectangle's height and width are a multiple of ten. the rectangles have to be passed on to the surface as in the given order in RecArray from left to right and from top to bottom. my problem is i can not find the x,y coordinates of the next rectangle. what im trying to do is, starting at the coordinate (0,0) i generate the first rectangle, add it to an arraylist RecList. Then i set the x and y coordinates. x becomes x = x+RecArray.get(0).getLength1() + 1. if x is greater than the width of the jpanel surface then it becomes 0 and y becomes y = y + 10 . starting from the second object in the RecArray i try to generate rectangles with the given coordinates and width&height. Then i try to compare them with all the previous rectangles to see if there is any overlapping. if there is no overlapping, the rectangle will be drawn, if there is overlapping, the x coordinate of the rec becomes x = RecList.get(j).width+1 and if that exceeds the width x becomes 0 and y is y=y+10. Then i regenate the current rectangle with the new coordinates and compare with the other rectangles in RecList again till i find the right spot for the current rectangle.ive been dealing with that issue for the last 5 days and am really fed up now. i would greatly appreciate any tipps. and Please be patient with me. im still learning programming.
super.paintComponent(g);
Graphics2D g2 = (Graphics2D) g;
Rectangle rec = new Rectangle(x, y, RecArray.get(0).getWidth(),
RecArray.get(0).getHeight());
RecList.add(rec);
recPaint(g2,RecArray.get(0));
x = x + RecArray.get(0).getWidth() + 1;
int i;
for (i = 1; i < RecArray.size(); i++) {
if (x >= this.getArea().getWidth()) {
x = 0;
y = y + 10;
}
Rectangle rec1 = new Rectangle(x, y, RecArray.get(i)
.getWidth(), RecArray.get(i).getheight());
for (int j= 0; j < RecList.size(); j++) {
if (!recIntersect(rec1, RecList.get(j))) {
RecList.add(rec1);
recPaint(g2,RecArray.get(i));
break;
}
else {
x = RecList.get(j).width;
if (x >= this.getFlaeche().getLength1()) {
x = 0;
y = y + 10;
}
rec1 = new Rectangle(x, y,RecArray.get(i). .getWidth(),
RecArray.get(i).getHeight());
}
x = x + RecArray.get(i).getWidth();
}
//With this method using the given rec parameter a rectangle will be drawn on the g2 and filled in blue colour
private void recPaint (Graphics2D g2, RecType rec){
g2.setColor(Color.BLUE);
g2.fillRect(x, y, rec.getWidth(),
rec.getLength2());
g2.setColor(Color.BLACK);
g2.drawRect(x, y, rec.getHeight(),
rec.getLength2());
}
// returns true, if two rectangles overlap
private boolean recIntersect(Rectangle rec1, Rectangle rec2) {
if( rec1.intersects(rec2)){
return true;
}
return false;
}
Edit: apparently i haven't stated clearly what my problem is. my problem is, that the way i generate (x,y) coordinates of the rectangles is obviously wrong. the way my algorithm works doesnt get the results i want. i want my rectangles to be placed neatly next to/above/below each other WITHOUT overlapping, which is not the case.

Separate out your List of Rectangles. Calculate the X, Y coordinates once.
Since I didn't have your object class, I used the Dimension class, which holds a width and a length. I used the Rectangle class to hold the objects that will eventually be drawn in your Swing GUI.
Divide and conquer. Separate out your GUI model, view, and controller(s). This way, you can focus on one piece of the puzzle at a time.
Here are the results of my test code when I ran it with a drawing area of 500, 400.
java.awt.Rectangle[x=0,y=0,width=100,height=100]
java.awt.Rectangle[x=100,y=0,width=20,height=10]
java.awt.Rectangle[x=120,y=0,width=40,height=20]
java.awt.Rectangle[x=160,y=0,width=60,height=40]
java.awt.Rectangle[x=220,y=0,width=80,height=60]
java.awt.Rectangle[x=300,y=0,width=20,height=10]
java.awt.Rectangle[x=320,y=0,width=120,height=110]
Here are the results of my test code when I ran it with a drawing area of 200, 200.
java.awt.Rectangle[x=0,y=0,width=100,height=100]
java.awt.Rectangle[x=100,y=0,width=20,height=10]
java.awt.Rectangle[x=120,y=0,width=40,height=20]
java.awt.Rectangle[x=0,y=100,width=60,height=40]
java.awt.Rectangle[x=60,y=100,width=80,height=60]
java.awt.Rectangle[x=140,y=100,width=20,height=10]
And here's the code. I fit rectangles on the X axis until I can't fit another rectangle. Then I add the maximum height to Y, reset the X to zero, reset the maximum height and fit the next row of rectangles.
Create test applications like I did here and make sure that you can create the GUI model long before you create the GUI view and GUI controller.
package com.ggl.testing;
import java.awt.Dimension;
import java.awt.Rectangle;
import java.util.ArrayList;
import java.util.List;
public class CalculatingRectangles {
public static void main(String[] args) {
CalculatingRectangles calculatingRectangles = new CalculatingRectangles();
Dimension drawingArea = new Dimension(200, 200);
List<Dimension> dimensions = new ArrayList<>();
dimensions.add(new Dimension(100, 100));
dimensions.add(new Dimension(20, 10));
dimensions.add(new Dimension(40, 20));
dimensions.add(new Dimension(60, 40));
dimensions.add(new Dimension(80, 60));
dimensions.add(new Dimension(20, 10));
dimensions.add(new Dimension(120, 110));
List<Rectangle> rectangles = calculatingRectangles
.calculatingRectangles(drawingArea, dimensions);
System.out.println(displayRectangles(rectangles));
}
private static String displayRectangles(List<Rectangle> rectangles) {
StringBuilder builder = new StringBuilder();
for (Rectangle r : rectangles) {
builder.append(r);
builder.append(System.getProperty("line.separator"));
}
return builder.toString();
}
public List<Rectangle> calculatingRectangles(Dimension drawingArea,
List<Dimension> dimensions) {
int width = drawingArea.width;
int height = drawingArea.height;
int x = 0;
int y = 0;
int index = 0;
int maxHeight = 0;
boolean hasRoom = dimensions.size() > index;
List<Rectangle> rectangles = new ArrayList<>();
while (hasRoom) {
Dimension d = dimensions.get(index);
maxHeight = Math.max(maxHeight, d.height);
if ((x + d.width) <= width && (y + maxHeight) <= height) {
Rectangle r = new Rectangle(x, y, d.width, d.height);
x += d.width;
rectangles.add(r);
index++;
if (index >= dimensions.size()) {
hasRoom = false;
}
} else {
y += maxHeight;
if (y > height) {
hasRoom = false;
}
x = 0;
}
}
return rectangles;
}
}

My method scale isn't working, what may be the issue?

I have been trying to scale a Shape in java, but I'm having some problems. When i try it the Shape simple dissapears... This method receives 2 points, toScale is the point that i want the shape to extend to, and p1 is the point that I clicked in the rectangle that is around the shape to select (there's a rectangle(boundingBox) surrounding the shape wheter is a polygone or a rectangle or just polylines)
Here's the scale method code:
public void scale(Point toScale, Point p1) {
Graphics g = parent.getGraphics();
int distanceToClicked = 0;
int distanceToBoundingBox = 0;
int scaleFactor = 0;
Vector<Point> pointsAux = new Vector<Point>();
Iterator<Point> it = points.iterator();
while (it.hasNext()){
Point p = it.next();
distanceToClicked = (int) Math.sqrt(Math.pow(getCentroid().getX()-p1.getX(), 2)+Math.pow(getCentroid().getY()-p1.getY(),2));
distanceToBoundingBox = (int) Math.sqrt(Math.pow(getCentroid().getX()-toScale.getX(),2)+Math.pow(getCentroid().getY()-toScale.getY(),2));
scaleFactor = distanceToClicked/distanceToBoundingBox;
p = new Point((int)p.getX()*scaleFactor,(int) p.getY()*scaleFactor);
pointsAux.add(p);
}
points.clear();
points.addAll(pointsAux);
}
public Point getCentroid(){
int sumx = 0;
int sumy = 0;
for(int i = 0; i<points.size();i++){
sumx+=points.get(i).getX();
sumy+=points.get(i).getY();
}
Point centroid = new Point(sumx/points.size(), sumy/points.size());
return centroid;
}
Any help would be appreciated
Thanks in advance, and eventually I'm sorry for the misunderstanding code

Something like that would do the trick:
public Collection<Point> scaleShape(float scale, Collection<Point> shape) {
Point centroid = getCentroid();
Collection<Point> scaledShape = new ArrayList<>(shape.size());
for (Point point : shape) {
Point diff = new Point(point.x() - centroid.x(), point.y() - centroid.y());
Point scaledPoint = new Point(
(int) (centroid.x() + scale * diff.x()),
(int) (centroid.y() + scale * diff.y()));
scaledShape.add(scaledPoint);
}
return scaledShape;
}
Basically, every points make a linear function with the centroid. Centroid's relative x = 0, while the current computed point is at relative x = 1. You want to find the point if it were at relative x = scale.