SwiftUI Animation's timingcurve creation - swift

Along with predefined animation curves these is an option to set a timing curve using timingcurve(::::duration:).
What is the meaning of its parameters (c0x,c0y, c1x, c1y)? How is the curve built? Documentation is lacking.

I'm only guessing as much as I can with the information we're given.
From the docs...
static func timingCurve(_ c0x: Double, _ c0y: Double, _ c1x: Double, _ c1y: Double, duration: Double = 0.35) -> Animation
It looks like the four numbers are actually a pair of x, y coordinates.
c0 = (c0x, c0y)
c1 = (c1x, c1y)
We also know that this is going to generate an easing curve which will start at time 0, animation %age 0 and end at time 1, animation %age 100.
So... I'm guessing these parameters are control points for a cubic bezier curve.
We would have four control points.
The start point (0, 0)
The first parameter c0
The second parameter c1
The end point (1, 1)
So, you need to provide the control points to generate the cubic curve that would describe the timing curve that you would like to use.
You can use this website https://cubic-bezier.com/#.17,.67,.82,.38 to have a look at how those properties change the curve.
As a basic example a timing curve like "ease-in-out" with a duration of 1 second would use parameters like...
timingCurve(0.42, 0, 0.58, 1, duration: 1.0)
Hope that helps.

Related

SCNNode Rotation Multiple Axes

This Question was posted, but never answered.
Similar to This Question, I am trying to understand SCNNode.rotation as a 4D vector. The prior question utilizes an example that only manipulates 1 axis, i.e.,
SCNNode.rotation = (0, 0, 1, degToRad(45)) //Rotate about z-axis by 45 degrees
which makes sense; however, what if I wanted to rotate the X axis by 20 degrees, Y axis by 45 degrees and then Z axis by 78 degrees?
SCNNode.rotation = ??
I would provide code I've tried, but I don't understand conceptually the notion of a 4D rotation vector.
Every node just has a transform with 4x4 matrix. So all the rotation operations are reflecting in the changing the transform.
In this case, if you change either of rotation, eulerAngles and orientation, you are supposed to get same value.
If rotating about three axises, I suggested using eulerAngles.
node.eulerAnges = SCNVector3(x:degToRad(20),y:degToRad(45), z:degToRad(78))
After you set this, go back and check to value of rotation:
SCNVector4(x: -0.16975601, y: 0.5943193, z: 0.786109, w: 1.448788)
This means there is an axis going through point(-0.16975601, 0.5943193, 0.786109) and origin (0,0,0), and node is rotating around it for 1.448788 (82 degree).

Understanding ARKit World Transform Matrices

In ARKit, when I perform a hit-test, I get back an instance of ARHitTestResult. One of the properties of this is worldTransform, which I understand contains a 4x4 transformation matrix of the position of the object – simd_float4x4.
As someone who is very unfamiliar with linear algebra and 3D graphics, how would I edit this matrix to, say, increase its y coordinate by 0.05?
If there is a blog post or something I could look at that would help me wrap my head around this, please let me know. I am not sure what terms I should be googling.
Sorry if my question is full of misunderstandings! As you can probably tell, I am not too familiar with these concepts.
Thank you to anyone who helps.
EDIT: The original question is best addressed by just adding 0.05 to the y component of the node's position. However, the original answer below does address a bit about composing transformation matrices, if that is something you are interested in.
======================================================================
If you want to apply an operation to a matrix, the most immediately simple way is to make a matrix that does that operation, and then multiply your original matrix by that new matrix.
For a translation, assuming you want to translate by x, y, z, you can do this:
let translation = simd_float4x4(
float4(1, 0, 0, 0),
float4(0, 1, 0, 0),
float4(0, 0, 1, 0),
float4(x, y, z, 1)
)
Note that this is just an identity matrix (1 down the diagonal) with the last column (!!!important, the float4s above are COLUMNS, not ROWS, as they would visually seem) set to contain the x/y/z values. You can research further into homogeneous coordinates, but think of this as just how a translation is represented.
Then, in simd, just do this: let newWorldTransform = translation * oldWorldTransform and you will have the old world transform translated by your x/y/z translation values (in your example, [x, y, z] = [0, 0.05, 0]).
However, it may be worth exploring why you want to edit your hit test results. I cannot think of a practical use case for that, so maybe if you explain a bit more about what you are trying to do I could suggest a more intuitive way to do it.
Matrices in 3D graphics is a regular way to translate, rotate, scale and shear 3D objects. In ARKit, RealityKit and SceneKit for consistent linear transformations you need to use simd_float4x4-like matrices:
var myMatrix: simd_float4x4
Translation 4x4 Matrix has 16 elements inside – 4 elements (float4) by 4 columns. Columns indices are 0, 1, 2 and 3. Translation matrix uses the fourth column with index 3.
SceneKit example
Use the following code to place your model 25 cm above its default position SCNVector3(0,0,0):
let sphereNode = SCNNode()
sphereNode.geometry = SCNSphere(radius: 1.0)
sphereNode.geometry?.firstMaterial?.diffuse.contents = UIColor.red
scene.rootNode.addChildNode(sphereNode)
var translation = matrix_identity_float4x4
translation.columns.3.y = 0.25
sphereNode.simdWorldTransform = translation
RealityKit example
let model = ModelEntity(mesh: .generateBox(size: 0.3))
let anchor = AnchorEntity()
anchor.addChild(model)
let currentMatrix = anchor.transform.matrix
var positionMatrix = simd_float4x4()
positionMatrix.columns.3.y = 0.25
let transform = simd_mul(currentMatrix, positionMatrix)
anchor.move(to: transform, relativeTo: model, duration: 1.0)

Rotate geometry around its local axis

I tried to rotate a geometry around its local axis, but haven't found a way to do so. I know that there is ST_Rotate (see https://postgis.net/docs/ST_Rotate.html) for 2D calculations and (among others) ST_RotateX (see https://postgis.net/docs/ST_RotateX.html), but these methods rotate a geometry around the origin. I also tried to abuse ST_Affine when I tried to change (what seems to be) the origin (namely 0/0/0):
SELECT ST_Affine(
ST_GeomFromText(ST_AsText(runway_area)),
1, 0, 0, 0,
cos(rotRadians), -sin(rotRadians), 0, sin(rotRadians), cos(rotRadians),
--- use the geometry's centroid instead of 0, 0, 0
ST_X(ST_GeomFromText(ST_AsText(runway_area))), ST_Y(ST_GeomFromText(ST_AsText(runway_area))), ST_Z(ST_GeomFromText(ST_AsText(runway_area)))
)
It didn't work out - all I got was something that was way away from the intended location. Do I miss a very fundamental method by PostGIS here to rotate a geometry around one of its local axis?
Take a closer look at ST_Rotate, and note that there are three argument signatures:
geometry ST_Rotate(geometry geomA, float rotRadians);
geometry ST_Rotate(geometry geomA, float rotRadians, float x0, float y0);
geometry ST_Rotate(geometry geomA, float rotRadians, geometry pointOrigin);
The x0 and y0 or pointOrigin arguments for the last two signatures do what your questions asks: they allow the rotation to pivot around a custom defined coordinate.
And an example from the docs show how to rotate a geometry 60 degrees clockwise around the centroid:
SELECT ST_AsEWKT(ST_Rotate(geom, radians(-60.0), ST_Centroid(geom)))
FROM (SELECT 'LINESTRING (50 160, 50 50, 100 50)'::geometry AS geom) AS foo;
st_asewkt
--------------------------------------------------------------
LINESTRING(116.4225 130.6721,21.1597 75.6721,46.1597 32.3708)
(1 row)
You could combine ST_Rotate with ST_Centroid, example:
ST_Rotate(ST_GeomFromText(ST_AsText(runway_area)), -pi()/3, ST_Centroid(ST_GeomFromText(ST_AsText(runway_area)))
The last three arguments to ST_Affine do not represent the origin, but the global "shift" in the affine transformation. The documentation for ST_RotateX shows how to use this function to generate a rotation around the x-axis. All these parameters are zero since it's a rotation without translation.
If you want to employ a general axis, you would need to construct the corresponding rotation matrix and substitute its elements for the arguments a,b,c,d,e,f,g,h,i of ST_Affine and set xoff, yoff, zoff to zero.

How to linearly interpolate animation curve in unity 3D?

After researching for hours and hours I am just not able to linearly interpolate two animation curve,I need something like Mathf.lerp for animation curve,I had try with inTangent and OutTangent with keyframes of the animation curve but it does not store the values,am I missing something ?
Need guidance,this would help me a lot in my project,thanks.
Seems to me you are looking to "morph" one animation curve into another. This imho depends on your use case.
Assuming both curves are defined between [0.0, 1.0], I'd calculate the curve value for t in both, and interpolate linearly both results over the same time.
/*
* Evaluates two AnimationCurve objects, and interpolates linearly
* between the results, effectively "morphing" from curve A to curve
* B in a linear fashion.
* Both curves must be defined between 0.0 and 1.0, and t must be
* within the same 0.0-1.0 range too.
*/
public float EvaluateLerpTwoCurves(AnimationCurve a, AnimationCurve b, float t) {
float valueA = a.Evaluate (t);
float valueB = b.Evaluate (t);
float result = Mathf.Lerp(valueA, valueB, t);
return result;
}
You may wish to interpolate between both AnimationCurve using a different approach (not linearly like Mathf.Lerp does), you could even use a third AnimationCurve to define how to morph between both curves.
Note that the suggested code above requires both curves to be defined between 0.0 and 1.0, and t must be within the same 0.0-1.0 range too.

Draw Camera Range with Postgis

i am working on some camera data. I have some points which consist of azimuth, angle, distance, and of course coordinate field attributes. In postgresql postgis I want to draw shapes like this with functions.
how can i draw this pink range shape?
at first should i draw 360 degree circle then extracting out of my shape... i dont know how?
I would create a circle around the point(x,y) with your radius distance, then use the info below to create a triangle that has a larger height than the radius.
Then using those two polygons do an ST_Intersection between the two geometries.
NOTE: This method only works if the angle is less than 180 degrees.
Note, that if you extend the outer edges and meet it with a 90 degree angle from the midpoint of your arc, you have a an angle, and an adjacent side. Now you can SOH CAH TOA!
Get Points B and C
Let point A = (x,y)
To get the top point:
point B = (x + radius, y + (r * tan(angle)))
to get the bottom point:
point C = (x + radius, y - (r * tan(angle)))
Rotate your triangle to you azimouth
Now that you have the triangle, you need to rotate it to your azimuth, with a pivot point of A. This means you need point A at the origin when you do the rotation. The rotation is the trickiest part. Its used in computer graphics all the time. (Actually, if you know OpenGL you could get it to do the rotation for you.)
NOTE: This method rotates counter-clockwise through an angle (theta) around the origin. You might have to adjust your azimuth accordingly.
First step: translate your triangle so that A (your original x,y) is at 0,0. Whatever you added/subtracted to x and y, do the same for the other two points.
(You need to translate it because you need point A to be at the origin)
Second step: Then rotate points B and C using a rotation matrix. More info here, but I'll give you the formula:
Your new point is (x', y')
Do this for points B and C.
Third step: Translate them back to the original place by adding or subtracting. If you subtracted x last time, add it this time.
Finally, use points {A,B,C} to create a triangle.
And then do a ST_Intersection(geom_circle,geom_triangle);
Because this takes a lot of calculations, it would be best to write a program that does all these calculations and then populates a table.
PostGIS supports curves, so one way to achieve this that might require less math on your behalf would be to do something like:
SELECT ST_GeomFromText('COMPOUNDCURVE((0 0, 0 10), CIRCULARSTRING(0 10, 7.071 7.071, 10 0), (10 0, 0 0))')
This describes a sector with an origin at 0,0, a radius of 10 degrees (geographic coordinates), and an opening angle of 45°.
Wrapping that with additional functions to convert it from a true curve into a LINESTRING, reduce the coordinate precision, and to transform it into WKT:
SELECT ST_AsText(ST_SnapToGrid(ST_CurveToLine(ST_GeomFromText('COMPOUNDCURVE((0 0, 0 10), CIRCULARSTRING(0 10, 7.071 7.071, 10 0), (10 0, 0 0))')), 0.01))
Gives:
This requires a few pieces of pre-computed information (the position of the centre, and the two adjacent vertices, and one other point on the edge of the segment) but it has the distinct advantage of actually producing a truly curved geometry. It also works with segments with opening angles greater than 180°.
A tip: the 7.071 x and y positions used in the example can be computed like this:
x = {radius} cos {angle} = 10 cos 45 ≈ 7.0171
y = {radius} sin {angle} = 10 sin 45 ≈ 7.0171
Corner cases: at the antimeridian, and at the poles.