Update screenshots, README

Author: nsh07

README.md

@@ -1,9 +1,41 @@
 # SimplyGraph
 
-#### This project is in very early development, and most features are not yet ready
+A simple, fast graphing calculator for Android
+
+Follows the latest Material 3 design guidelines and adapts to the system color (Material You)
+
+Supports explicit and implicit functions and relations, polar functions, and parametric relations
+
+## Screenshots
 
 <p width="100%">
-<img src="screenshot.png" width="30%">
-<img src="screenshot2.png" width="30%">
-<img src="screenshot3.png" width="30%">
-</p>
+<img src="screenshot.png" width="24%">
+<img src="screenshot2.png" width="24%">
+<img src="screenshot3.png" width="24%">
+<img src="screenshot4.png" width="24%">
+</p>
+
+## How it works
+
+This app utilises JNI to offload the graph point calculation to native C++ for extremely fast
+calculation of points (at least a few orders of magnitude improvement over Kotlin code in my own
+benchmarks). The basic layout of how it works is:
+
+- (Steps)
+
+1. Function string input by user
+2. JNI function called: Function string, canvas geometry data, scale and offset are passed
+3. JNI performs C++ function call passing all the data
+4. C++ function returns std::vector<float> containing point data
+5. JNI returns array of floats
+6. Points are plotted on Jetpack Compose Canvas
+
+The exact working is slightly more complex, for example the C++ point calculation function analyses
+the function string to determine whether it is explicit, implicit, polar or parametric and performs
+the calculations accordingly, and also simplifies the graph if there are too many points to save
+memory and drawing time.
+
+### Special thanks
+
+- This app uses [ExprTk](https://github.com/ArashPartow/exprtk) to evaluate mathematical
+  expressions. Thanks to Arash Partow for creating this library.

app/src/main/java/org/nsh07/simplygraph/ui/AppScreen.kt

@@ -48,6 +48,7 @@ import androidx.compose.ui.Modifier
 import androidx.compose.ui.draw.clipToBounds
 import androidx.compose.ui.geometry.Offset
 import androidx.compose.ui.graphics.PointMode
+import androidx.compose.ui.graphics.StrokeCap
 import androidx.compose.ui.res.painterResource
 import androidx.compose.ui.text.input.ImeAction
 import androidx.compose.ui.text.style.TextAlign
@@ -68,7 +69,7 @@ fun AppScreen(modifier: Modifier = Modifier) {
 
     val expandSheet = remember(functionsState.function) {
         functionsState.function.matches(
-            "\\s*r\\s*=\\s*\\S+\\s*|\\s*\\(\\s*\\S+\\s*,\\s*\\S+\\s*\\)\\s*".toRegex()
+            "\\s*r\\s*=.+|\\s*\\(.+,.+\\)\\s*".toRegex()
         )
     }
 
@@ -282,7 +283,8 @@ fun AppScreen(modifier: Modifier = Modifier) {
                             PointMode.Points
                         else PointMode.Polygon,
                     color = colorScheme.primary,
-                    strokeWidth = 3.dp.toPx()
+                    strokeWidth = 3.dp.toPx(),
+                    cap = StrokeCap.Round
                 )
             }
             FloatingActionButton(