Update

Bukkit/build.gradle

@@ -14,7 +14,7 @@ repositories {
 
 dependencies {
     compileOnly 'org.spigotmc:spigot-api:1.19.2-R0.1-SNAPSHOT'
-    implementation project(':Commons')
+    implementation project(':Converter')
 }
 
 test {

Bukkit/src/main/java/io/github/simplexdev/paper/DataConverter.java

@@ -1,12 +1,12 @@
 package io.github.simplexdev.paper;
 
-import io.github.simplexdev.polarize.api.IPoint2D;
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
-import io.github.simplexdev.polarize.api.IPoint3D;
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
-import io.github.simplexdev.polarize.api.IScalar;
+import io.github.simplexdev.polarize.api.spatial.IScalar;
-import io.github.simplexdev.polarize.api.IVector;
+import io.github.simplexdev.polarize.api.spatial.IVector;
 import io.github.simplexdev.polarize.cartesian.CartesianVector;
-import io.github.simplexdev.polarize.math.Point2D;
+import io.github.simplexdev.polarize.cartesian.Point2D;
-import io.github.simplexdev.polarize.math.Point3D;
+import io.github.simplexdev.polarize.cartesian.Point3D;
 import io.github.simplexdev.polarize.polar.Scalar;
 import org.bukkit.Location;
 import org.bukkit.World;

Caravan/build.gradle

@@ -0,0 +1,19 @@
+plugins {
+    id 'java'
+}
+
+group = 'io.github.simplexdev'
+version = '1.0-SNAPSHOT'
+
+repositories {
+    mavenCentral()
+}
+
+dependencies {
+    testImplementation platform('org.junit:junit-bom:5.9.1')
+    testImplementation 'org.junit.jupiter:junit-jupiter'
+}
+
+test {
+    useJUnitPlatform()
+}

Caravan/src/main/java/io/github/simplexdev/caravan/CaravanAPI.java

@@ -0,0 +1,5 @@
+package io.github.simplexdev.caravan;
+
+public interface CaravanAPI {
+
+}

Caravan/src/main/java/io/github/simplexdev/caravan/api/Graph.java

@@ -0,0 +1,4 @@
+package io.github.simplexdev.caravan.api;
+
+public interface Graph {
+}

Caravan/src/main/java/io/github/simplexdev/caravan/api/Mapper.java

@@ -0,0 +1,12 @@
+package io.github.simplexdev.caravan.api;
+
+import io.github.simplexdev.caravan.api.curve.GenericCurve;
+import io.github.simplexdev.caravan.spatial.Point;
+
+import java.util.Set;
+
+public interface Mapper {
+    <T extends GenericCurve> Set<Point> generateCurve(T curve);
+
+
+}

Caravan/src/main/java/io/github/simplexdev/caravan/api/curve/GenericCurve.java

@@ -0,0 +1,31 @@
+package io.github.simplexdev.caravan.api.curve;
+
+import io.github.simplexdev.caravan.spatial.Point;
+
+import java.util.LinkedHashSet;
+
+public interface GenericCurve {
+    LinkedHashSet<Point> linkedPoints();
+
+    default void addPoint(Point point) {
+        linkedPoints().add(point);
+    }
+
+    default void removePoint(Point point) {
+        linkedPoints().remove(point);
+    }
+
+    default void clearPoints() {
+        linkedPoints().clear();
+    }
+
+    default boolean containsPoint(Point point) {
+        return linkedPoints().contains(point);
+    }
+
+    default void addPoints(Point... points) {
+        for (Point point : points) {
+            addPoint(point);
+        }
+    }
+}

Caravan/src/main/java/io/github/simplexdev/caravan/api/curve/Helix.java

@@ -0,0 +1,25 @@
+package io.github.simplexdev.caravan.api.curve;
+
+import io.github.simplexdev.caravan.spatial.Point;
+
+public interface Helix extends GenericCurve {
+    double getRadius();
+
+    double getDistance();
+
+    default double getX(double pos) {
+        return getRadius() * Math.cos(pos);
+    }
+
+    default double getY(double pos) {
+        return getRadius() * Math.sin(pos);
+    }
+
+    default double getZ(double pos) {
+        return getDistance() * pos;
+    }
+
+    default Point toPoint(double pos) {
+        return new Point(getX(pos), getY(pos), getZ(pos));
+    }
+}

Caravan/src/main/java/io/github/simplexdev/caravan/api/curve/Torus.java

@@ -0,0 +1,11 @@
+package io.github.simplexdev.caravan.api.curve;
+
+public interface Torus {
+    double getDistanceFromCenter();
+
+    double getRadius();
+
+    default double getX() {
+
+    }
+}

Caravan/src/main/java/io/github/simplexdev/caravan/base/Caravan.java

@@ -0,0 +1,11 @@
+package io.github.simplexdev.caravan.base;
+
+import io.github.simplexdev.caravan.CaravanAPI;
+
+public final class Caravan implements CaravanAPI {
+    private static final CaravanAPI api = new Caravan();
+
+    public static CaravanAPI getAPI() {
+        return api;
+    }
+}

Caravan/src/main/java/io/github/simplexdev/caravan/spatial/Point.java

@@ -0,0 +1,65 @@
+package io.github.simplexdev.caravan.spatial;
+
+public class Point {
+    private final double x;
+    private final double y;
+    private final double z;
+
+    private double xOffset;
+    private double yOffset;
+    private double zOffset;
+
+    public Point(double x, double y, double z) {
+        this.x = x;
+        this.y = y;
+        this.z = z;
+        this.xOffset = 0;
+        this.yOffset = 0;
+        this.zOffset = 0;
+    }
+
+    public Point(double x, double y, double z, double xOffset, double yOffset, double zOffset) {
+        this.x = x;
+        this.y = y;
+        this.z = z;
+        this.xOffset = xOffset;
+        this.yOffset = yOffset;
+        this.zOffset = zOffset;
+    }
+
+    public double getX() {
+        return x;
+    }
+
+    public double getY() {
+        return y;
+    }
+
+    public double getZ() {
+        return z;
+    }
+
+    public double getXOffset() {
+        return xOffset;
+    }
+
+    public void setXOffset(double xOffset) {
+        this.xOffset = xOffset;
+    }
+
+    public double getYOffset() {
+        return yOffset;
+    }
+
+    public void setYOffset(double yOffset) {
+        this.yOffset = yOffset;
+    }
+
+    public double getZOffset() {
+        return zOffset;
+    }
+
+    public void setZOffset(double zOffset) {
+        this.zOffset = zOffset;
+    }
+}

Commons/build.gradle

@@ -1,10 +0,0 @@
-plugins {
-    id 'java'
-}
-
-group = 'io.github.simplexdev'
-version = '1.0-SNAPSHOT'
-
-test {
-    useJUnitPlatform()
-}

Commons/src/main/java/io/github/simplexdev/polarize/api/IPoint3D.java

@@ -1,30 +0,0 @@
-package io.github.simplexdev.polarize.api;
-
-/**
- * Represents a point in 3D space.
- * It's important to note that Y is our vertical plane, and XZ is our horizontal plane.
- * This is because Minecraft's coordinate system is based on the XZ plane.
- * While this library is not Minecraft-specific, it is designed with Minecraft in mind.
- */
-public interface IPoint3D {
-    /**
-     * Returns the X coordinate of this point.
-     *
-     * @return The X coordinate of this point.
-     */
-    double getX();
-
-    /**
-     * Returns the Y coordinate of this point.
-     *
-     * @return The Y coordinate of this point.
-     */
-    double getY();
-
-    /**
-     * Returns the Z coordinate of this point.
-     *
-     * @return The Z coordinate of this point.
-     */
-    double getZ();
-}

Commons/src/main/java/io/github/simplexdev/polarize/math/Point2D.java

@@ -1,24 +0,0 @@
-package io.github.simplexdev.polarize.math;
-
-import io.github.simplexdev.polarize.api.IPoint2D;
-
-public class Point2D implements IPoint2D {
-
-    private final double x;
-    private final double z;
-
-    public Point2D(double x, double z) {
-        this.x = x;
-        this.z = z;
-    }
-
-    @Override
-    public double getX() {
-        return this.x;
-    }
-
-    @Override
-    public double getZ() {
-        return this.z;
-    }
-}

Commons/src/main/java/io/github/simplexdev/polarize/math/Point3D.java

@@ -1,30 +0,0 @@
-package io.github.simplexdev.polarize.math;
-
-import io.github.simplexdev.polarize.api.IPoint3D;
-
-public class Point3D implements IPoint3D {
-    private final double x;
-    private final double y;
-    private final double z;
-
-    public Point3D(double x, double y, double z) {
-        this.x = x;
-        this.y = y;
-        this.z = z;
-    }
-
-    @Override
-    public double getX() {
-        return x;
-    }
-
-    @Override
-    public double getY() {
-        return y;
-    }
-
-    @Override
-    public double getZ() {
-        return z;
-    }
-}

Converter/.gitignore

@@ -0,0 +1,42 @@
+.gradle
+build/
+!gradle/wrapper/gradle-wrapper.jar
+!**/src/main/**/build/
+!**/src/test/**/build/
+
+### IntelliJ IDEA ###
+.idea/modules.xml
+.idea/jarRepositories.xml
+.idea/compiler.xml
+.idea/libraries/
+*.iws
+*.iml
+*.ipr
+out/
+!**/src/main/**/out/
+!**/src/test/**/out/
+
+### Eclipse ###
+.apt_generated
+.classpath
+.factorypath
+.project
+.settings
+.springBeans
+.sts4-cache
+bin/
+!**/src/main/**/bin/
+!**/src/test/**/bin/
+
+### NetBeans ###
+/nbproject/private/
+/nbbuild/
+/dist/
+/nbdist/
+/.nb-gradle/
+
+### VS Code ###
+.vscode/
+
+### Mac OS ###
+.DS_Store

Converter/build.gradle

@@ -0,0 +1,15 @@
+plugins {
+    id 'java'
+}
+
+group = 'io.github.simplexdev'
+version = '1.0-SNAPSHOT'
+
+dependencies {
+    implementation 'org.jetbrains:annotations:24.0.0'
+    testImplementation 'org.mockito:mockito-core:4.11.0'
+}
+
+test {
+    useJUnitPlatform()
+}

Converter/src/main/java/io/github/simplexdev/polarize/api/rotation/IAxisAngle.java

@@ -0,0 +1,19 @@
+package io.github.simplexdev.polarize.api.rotation;
+
+import io.github.simplexdev.polarize.api.units.Theta;
+
+public interface IAxisAngle {
+    double getX();
+
+    double getY();
+
+    double getZ();
+
+    Theta getAngle();
+
+    IAxisAngle negate();
+
+    IAxisAngle normalize();
+
+    IAxisAngle inverse();
+}

Converter/src/main/java/io/github/simplexdev/polarize/api/rotation/IQuaternion.java

@@ -1,4 +1,6 @@
-package io.github.simplexdev.polarize.api;
+package io.github.simplexdev.polarize.api.rotation;
+
+import io.github.simplexdev.polarize.api.spatial.IVector;
 
 /**
  * Represents the rotation of an object in 3D space.

Converter/src/main/java/io/github/simplexdev/polarize/api/spatial/IPoint2D.java

@@ -1,4 +1,7 @@
-package io.github.simplexdev.polarize.api;
+package io.github.simplexdev.polarize.api.spatial;
+
+import static io.github.simplexdev.polarize.api.units.Point.X;
+import static io.github.simplexdev.polarize.api.units.Point.Z;
 
 /**
  * Represents a point in 2D space along an XZ plane.
@@ -11,12 +14,12 @@ public interface IPoint2D {
      *
      * @return The X coordinate of the point.
      */
-    double getX();
+    X getX();
 
     /**
      * Returns the Z coordinate of the point.
      *
      * @return The Z coordinate of the point.
      */
-    double getZ();
+    Z getZ();
 }

Converter/src/main/java/io/github/simplexdev/polarize/api/spatial/IPoint3D.java

@@ -0,0 +1,86 @@
+package io.github.simplexdev.polarize.api.spatial;
+
+import java.util.Set;
+import static io.github.simplexdev.polarize.api.units.Point.*;
+
+/**
+ * Represents a point in 3D space.
+ * It's important to note that Y is our vertical plane, and XZ is our horizontal plane.
+ * This is because Minecraft's coordinate system is based on the XZ plane.
+ * While this library is not Minecraft-specific, it is designed with Minecraft in mind.
+ */
+public interface IPoint3D {
+    /**
+     * Returns the X coordinate of this point.
+     *
+     * @return The X coordinate of this point.
+     */
+    X getX();
+
+    /**
+     * Returns the Y coordinate of this point.
+     *
+     * @return The Y coordinate of this point.
+     */
+    Y getY();
+
+    /**
+     * Returns the Z coordinate of this point.
+     *
+     * @return The Z coordinate of this point.
+     */
+    Z getZ();
+
+    /**
+     * Returns the distance between this point and another point.
+     *
+     * @param point The point to calculate the distance to.
+     * @return The distance between this point and the other point.
+     */
+    IVector getDistance(IPoint3D point);
+
+    /**
+     * Returns the difference between this point and another point.
+     *
+     * @param point The point to calculate the difference to.
+     * @return The difference between this point and the other point.
+     */
+    IPoint3D getDifferential(IPoint3D point);
+
+    /**
+     * Returns the sum of this point and another point.
+     *
+     * @param point The point to add to this point.
+     * @return The sum of this point and the other point.
+     */
+    IPoint3D add(IPoint3D point);
+
+    /**
+     * Returns the product of this point and another point.
+     * This will effectively scale the point by the other point.
+     * For example, if this point is (1, 1, 1) and the other point is (2, 2, 2),
+     * the resulting point will be (2, 2, 2).
+     *
+     * @param point The point to multiply this point by.
+     * @return The product of this point and the other point.
+     */
+    IPoint3D multiply(IPoint3D point);
+
+    /**
+     * Translates this point according to the vector provided.
+     * This will effectively move the point to the desired destination defined by the vector.
+     *
+     * @param vector The vector to add to this point.
+     * @return The sum of this point and the vector.
+     */
+    IPoint3D move(IVector vector);
+
+    /**
+     * Returns the midpoint between this point and another point.
+     *
+     * @param point     The point to calculate the midpoint to.
+     * @param numPoints The number of points to draw between this point and the other point.
+     * @return The midpoint between this point and the other point.
+     */
+    Set<IPoint3D> drawLine(IPoint3D point, double numPoints);
+}

Converter/src/main/java/io/github/simplexdev/polarize/api/spatial/IScalar.java

@@ -1,4 +1,6 @@
-package io.github.simplexdev.polarize.api;
+package io.github.simplexdev.polarize.api.spatial;
+
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
 
 /**
  * Represents a scalar value.

Converter/src/main/java/io/github/simplexdev/polarize/api/spatial/IVector.java

@@ -1,5 +1,8 @@
-package io.github.simplexdev.polarize.api;
+package io.github.simplexdev.polarize.api.spatial;
 
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
+import io.github.simplexdev.polarize.api.units.Point;
+import io.github.simplexdev.polarize.cartesian.Point3D;
 import org.jetbrains.annotations.NotNull;
 
 /**
@@ -149,4 +152,32 @@ public interface IVector {
      * @return A new vector with the X Y Z mods rotated by the quaternion passed in.
      */
     IVector rotate(@NotNull IQuaternion quaternion);
+
+    /**
+     * This method returns the destination point defined by the XYZ mods and the length of the vector.
+     * The destination point is calculated from the X Y Z mods as
+     * (x * length, y * length, z * length).
+     * The destination point is the point that the vector is pointing to.
+     *
+     * @return The destination point defined by the XYZ mods and the length of the vector.
+     */
+    default IPoint3D getDestination() {
+        return Point.fromDouble(getX() * length(), getY() * length(), getZ() * length());
+    }
+
+    /**
+     * This method returns a cross-product of this vector and the vector passed in.
+     * The cross-product is calculated from the X Y Z mods as
+     * (y * vector.getZ() - z * vector.getY(), z * vector.getX() - x * vector.getZ(), x * vector.getY() - y * vector.getX()).
+     *
+     * @param vector The vector to cross-product with.
+     * @return A cross-product of this vector and the vector passed in.
+     */
+    default IPoint3D cross(IVector vector) {
+        return Point.fromDouble(
+                getY() * vector.getZ() - getZ() * vector.getY(),
+                getZ() * vector.getX() - getX() * vector.getZ(),
+                getX() * vector.getY() - getY() * vector.getX()
+        );
+    }
 }

Converter/src/main/java/io/github/simplexdev/polarize/api/spatial/IVertex.java

@@ -0,0 +1,5 @@
+package io.github.simplexdev.polarize.api.spatial;
+
+public interface IVertex {
+
+}

Converter/src/main/java/io/github/simplexdev/polarize/api/units/Phi.java

@@ -20,4 +20,12 @@ public interface Phi {
      * @return the azimuth value as a double
      */
     double getAzimuth();
+
+    static Phi from(double y, Radius r) {
+        return () -> Math.cos(y / r.length());
+    }
+
+    static Phi of(double azimuth) {
+        return () -> azimuth;
+    }
 }

Converter/src/main/java/io/github/simplexdev/polarize/api/units/Point.java

@@ -0,0 +1,244 @@
+package io.github.simplexdev.polarize.api.units;
+
+
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.cartesian.Point2D;
+import io.github.simplexdev.polarize.cartesian.Point3D;
+import io.github.simplexdev.polarize.math.function.Integral;
+
+import java.io.Serializable;
+import java.util.function.DoubleUnaryOperator;
+
+@FunctionalInterface
+public interface Point extends Serializable {
+
+    /**
+     * Creates a 2d point from a given X and Z value.
+     *
+     * @param x The X value.
+     * @param z The Z value.
+     * @return The 2d point.
+     */
+    static IPoint2D fromXZ(X x, Z z) {
+        return new Point2D(x, z);
+    }
+
+    /**
+     * Creates a 3d point from a given X, Y, and Z value.
+     *
+     * @param x The X value.
+     * @param y The Y value.
+     * @param z The Z value.
+     * @return The 3d point.
+     */
+    static IPoint3D fromXYZ(X x, Y y, Z z) {
+        return new Point3D(x, y, z);
+    }
+
+    /**
+     * Creates a 2d point from the given double values.
+     *
+     * @param x The X value.
+     * @param z The Z value.
+     * @return The 2d point.
+     */
+    static IPoint2D fromDouble(double x, double z) {
+        return new Point2D(() -> x, () -> z);
+    }
+
+    /**
+     * Creates a 3d point from the given double values.
+     *
+     * @param x The X value.
+     * @param y The Y value.
+     * @param z The Z value.
+     * @return The 3d point.
+     */
+    static IPoint3D fromDouble(double x, double y, double z) {
+        return new Point3D(() -> x, () -> y, () -> z);
+    }
+
+    @Override
+    String toString();
+
+    /**
+     * Returns the numerical representation of the point.
+     *
+     * @return The value of the point.
+     */
+    double get();
+
+    /**
+     * Returns the distance between this point and the given point.
+     *
+     * @param point The point to compare to.
+     * @return The distance between the two points.
+     */
+    default double distance(double point) {
+        return Math.abs(this.get() - point);
+    }
+
+    /**
+     * Returns the distance between this point and the given point.
+     *
+     * @param point The point to compare to.
+     * @return The distance between the two points.
+     */
+    default double distance(Point point) {
+        return this.distance(point.get());
+    }
+
+    /**
+     * Adds the given point to this point.
+     *
+     * @param point The point to add.
+     * @return The sum of the two points.
+     */
+    default double add(double point) {
+        return this.get() + point;
+    }
+
+    /**
+     * Adds the given point to this point.
+     *
+     * @param point The point to add.
+     * @return The sum of the two points.
+     */
+    default double add(Point point) {
+        return this.add(point.get());
+    }
+
+    /**
+     * Subtracts the given point from this point.
+     *
+     * @param point The point to subtract.
+     * @return The difference of the two points.
+     */
+    default double subtract(double point) {
+        return this.get() - point;
+    }
+
+    /**
+     * Subtracts the given point from this point.
+     *
+     * @param point The point to subtract.
+     * @return The difference of the two points.
+     */
+    default double subtract(Point point) {
+        return this.subtract(point.get());
+    }
+
+    /**
+     * Multiplies this point by the given point.
+     *
+     * @param point The point to multiply by.
+     * @return The product of the two points.
+     */
+    default double multiply(double point) {
+        return this.get() * point;
+    }
+
+    /**
+     * Multiplies this point by the given point.
+     *
+     * @param point The point to multiply by.
+     * @return The product of the two points.
+     */
+    default double multiply(Point point) {
+        return this.multiply(point.get());
+    }
+
+    /**
+     * Divides this point by the given point.
+     *
+     * @param point The point to divide by.
+     * @return The quotient of the two points.
+     */
+    default double divide(double point) {
+        return this.get() / point;
+    }
+
+    /**
+     * Divides this point by the given point.
+     *
+     * @param point The point to divide by.
+     * @return The quotient of the two points.
+     */
+    default double divide(Point point) {
+        return this.divide(point.get());
+    }
+
+    /**
+     * Returns this point raised to the power of the given point.
+     *
+     * @param point The point to raise this point to.
+     * @return The power of the two points.
+     */
+    default double power(double point) {
+        return Math.pow(this.get(), point);
+    }
+
+    /**
+     * Returns this point raised to the power of the given point.
+     *
+     * @param point The point to raise this point to.
+     * @return The power of the two points.
+     */
+    default double power(Point point) {
+        return this.power(point.get());
+    }
+
+    /**
+     * Returns the integral of the given function from this point to the given point.
+     *
+     * @param point        The point to integrate to.
+     * @param subIntervals The number of sub-intervals to use.
+     * @param function     The function to integrate.
+     * @return The integral of the function.
+     */
+    default double integ(double point, double subIntervals, DoubleUnaryOperator function) {
+        return Integral.integrate(this.get(), point, subIntervals, function);
+    }
+
+    /**
+     * Returns the integral of the given function from this point to the given point.
+     *
+     * @param point        The point to integrate to.
+     * @param subIntervals The number of sub-intervals to use.
+     * @param function     The function to integrate.
+     * @return The integral of the function.
+     */
+    default double integ(Point point, double subIntervals, DoubleUnaryOperator function) {
+        return this.integ(point.get(), subIntervals, function);
+    }
+
+    /**
+     * Represents any value of X along the <u>X coordinate plane</u>.
+     */
+    @FunctionalInterface
+    interface X extends Point {
+        @Override
+        double get();
+    }
+
+    /**
+     * Represents any value of Y along the <u>Y coordinate plane</u>.
+     */
+    @FunctionalInterface
+    interface Y extends Point {
+
+        @Override
+        double get();
+    }
+
+    /**
+     * Represents any value of Z along the <u>Z coordinate plane</u>.
+     */
+    @FunctionalInterface
+    interface Z extends Point {
+
+        @Override
+        double get();
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/api/units/Radius.java

@@ -19,4 +19,12 @@ public interface Radius {
      * @return the length of the radius as a double
      */
     double length();
+
+    static Radius of(double length) {
+        return () -> length;
+    }
+
+    static Radius from(double x, double y, double z) {
+        return () -> Math.sqrt(x * x + y * y + z * z);
+    }
 }

Converter/src/main/java/io/github/simplexdev/polarize/api/units/Theta.java

@@ -11,4 +11,12 @@ public interface Theta {
      * @return the zenith angle as a double.
      */
     double getZenith();
+
+    static Theta from(double x, double z) {
+        return () -> Math.atan2(x, z);
+    }
+
+    static Theta of(double zenithAngle) {
+        return () -> zenithAngle;
+    }
 }

Converter/src/main/java/io/github/simplexdev/polarize/cartesian/CartesianUnit.java

@@ -1,9 +1,8 @@
 package io.github.simplexdev.polarize.cartesian;
 
-import io.github.simplexdev.polarize.api.IPoint2D;
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
-import io.github.simplexdev.polarize.api.IPoint3D;
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
-import io.github.simplexdev.polarize.math.Point2D;
+import io.github.simplexdev.polarize.api.units.Point;
-import io.github.simplexdev.polarize.math.Point3D;
 
 /**
  * CartesianUnit is a class that contains a 3D point and a 2D point
@@ -21,8 +20,8 @@ public class CartesianUnit {
      * @param z The z value of the 3D point and the 2D point.
      */
     public CartesianUnit(double x, double y, double z) {
-        this.point3d = new Point3D(x, y, z);
+        this.point3d = Point.fromDouble(x, y, z);
-        this.point2d = new Point2D(x, z);
+        this.point2d = Point.fromDouble(x, z);
     }
 
     /**

Converter/src/main/java/io/github/simplexdev/polarize/cartesian/CartesianVector.java

@@ -1,7 +1,7 @@
 package io.github.simplexdev.polarize.cartesian;
 
-import io.github.simplexdev.polarize.api.IQuaternion;
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
-import io.github.simplexdev.polarize.api.IVector;
+import io.github.simplexdev.polarize.api.spatial.IVector;
 import io.github.simplexdev.polarize.math.Quaternion;
 import org.jetbrains.annotations.NotNull;
 

Converter/src/main/java/io/github/simplexdev/polarize/cartesian/Point2D.java

@@ -0,0 +1,25 @@
+package io.github.simplexdev.polarize.cartesian;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
+import static io.github.simplexdev.polarize.api.units.Point.*;
+
+public class Point2D implements IPoint2D {
+
+    private final X x;
+    private final Z z;
+
+    public Point2D(X x, Z z) {
+        this.x = x;
+        this.z = z;
+    }
+
+    @Override
+    public X getX() {
+        return this.x;
+    }
+
+    @Override
+    public Z getZ() {
+        return this.z;
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/cartesian/Point3D.java

@@ -0,0 +1,102 @@
+package io.github.simplexdev.polarize.cartesian;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.api.spatial.IVector;
+import io.github.simplexdev.polarize.api.units.Point;
+import io.github.simplexdev.polarize.log.PolarizeLogger;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.LinkedHashSet;
+import java.util.Set;
+
+public class Point3D implements IPoint3D {
+    private final Point.X x;
+    private final Point.Y y;
+    private final Point.Z z;
+
+    public Point3D(Point.X x, Point.Y y, Point.Z z) {
+        this.x = x;
+        this.y = y;
+        this.z = z;
+    }
+
+    @Override
+    public Point.X getX() {
+        return x;
+    }
+
+    @Override
+    public Point.Y getY() {
+        return y;
+    }
+
+    @Override
+    public Point.Z getZ() {
+        return z;
+    }
+
+    @Override
+    public IVector getDistance(@NotNull IPoint3D point) {
+        return new CartesianVector(point.getX().subtract(x),
+                point.getY().subtract(y),
+                point.getZ().subtract(z));
+    }
+
+    @Override
+    public IPoint3D multiply(IPoint3D point) {
+        return new Point3D(() -> x.multiply(point.getX()),
+                () -> y.multiply(point.getY()),
+                () -> z.multiply(point.getZ()));
+    }
+
+    @Override
+    public IPoint3D move(IVector vector) {
+        return add(vector.getDestination());
+    }
+
+    @Override
+    public IPoint3D getDifferential(@NotNull IPoint3D point) {
+        return new Point3D(() -> point.getX().subtract(x),
+                () -> point.getY().subtract(y),
+                () -> point.getZ().subtract(z));
+    }
+
+    @Override
+    public IPoint3D add(IPoint3D point) {
+        return new Point3D(() -> point.getX().add(x),
+                () -> point.getY().add(y),
+                () -> point.getZ().add(z));
+    }
+
+    @Override
+    public Set<IPoint3D> drawLine(IPoint3D point, double numPoints) {
+        IPoint3D diff = getDifferential(point);
+        Set<IPoint3D> point3DSet = new LinkedHashSet<>();
+        for (double i = 0.0; i <= numPoints; i++) {
+            double multiplier = i / numPoints;
+            PolarizeLogger.info("i: " + i);
+            PolarizeLogger.info("multiplier: " + multiplier);
+            IPoint3D adjusted = Point.fromDouble(diff.getX().multiply(() -> multiplier),
+                    diff.getY().multiply(multiplier),
+                    diff.getZ().multiply(multiplier));
+            PolarizeLogger.info("adjusted: " + "X: " + adjusted.getX()
+                    + " Y: " + adjusted.getY()
+                    + " Z: " + adjusted.getZ());
+            IPoint3D added = this.add(adjusted);
+            PolarizeLogger.info("added: " + "X: " + added.getX()
+                    + " Y: " + added.getY()
+                    + " Z: " + added.getZ());
+            point3DSet.add(added);
+        }
+        return point3DSet;
+    }
+
+    public void drawLineTestMethod() {
+        IPoint3D origin = Point.fromDouble(2, 6, 5);
+        IPoint3D destination = Point.fromDouble(10, 6, -15);
+        origin.drawLine(destination, 25).forEach(point3D ->
+                PolarizeLogger.info("X: " + point3D.getX()
+                        + " Y: " + point3D.getY()
+                        + " Z: " + point3D.getZ()));
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/cartesian/Vertex.java

@@ -0,0 +1,24 @@
+package io.github.simplexdev.polarize.cartesian;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.api.spatial.IVector;
+
+public class Vertex {
+    private final IPoint3D vertex;
+
+    public Vertex(IVector vector1, IVector vector2) {
+        this.vertex = vector1.cross(vector2);
+    }
+
+    public double getX() {
+        return vertex.getX().get();
+    }
+
+    public double getY() {
+        return vertex.getY().get();
+    }
+
+    public double getZ() {
+        return vertex.getZ().get();
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/log/PolarizeLogger.java

@@ -0,0 +1,31 @@
+package io.github.simplexdev.polarize.log;
+
+import java.util.logging.Logger;
+
+public class PolarizeLogger {
+    private static final Logger logger = Logger.getLogger("Polarize");
+
+    private PolarizeLogger() {
+        throw new AssertionError();
+    }
+
+    public static void info(String message) {
+        logger.info(message);
+    }
+
+    public static void warning(String message) {
+        logger.warning(message);
+    }
+
+    public static void warning(Throwable throwable) {
+        logger.warning(throwable.getMessage());
+    }
+
+    public static void severe(String message) {
+        logger.severe(message);
+    }
+
+    public static void severe(Throwable throwable) {
+        logger.severe(throwable.getMessage());
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/math/AxisAngle.java

@@ -0,0 +1,54 @@
+package io.github.simplexdev.polarize.math;
+
+import io.github.simplexdev.polarize.api.rotation.IAxisAngle;
+import io.github.simplexdev.polarize.api.units.Theta;
+
+public class AxisAngle implements IAxisAngle {
+    private final double x;
+    private final double y;
+    private final double z;
+    private final Theta angle;
+
+    public AxisAngle(double x, double y, double z, Theta angle) {
+        this.x = x;
+        this.y = y;
+        this.z = z;
+        this.angle = angle;
+    }
+
+    @Override
+    public double getX() {
+        return this.x;
+    }
+
+    @Override
+    public double getY() {
+        return this.y;
+    }
+
+    @Override
+    public double getZ() {
+        return this.z;
+    }
+
+    @Override
+    public Theta getAngle() {
+        return this.angle;
+    }
+
+    @Override
+    public IAxisAngle negate() {
+        return new AxisAngle(-this.x, -this.y, -this.z, () -> -(this.angle.getZenith()));
+    }
+
+    @Override
+    public IAxisAngle normalize() {
+        double magnitude = Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z);
+        return new AxisAngle(this.x / magnitude, this.y / magnitude, this.z / magnitude, this.angle);
+    }
+
+    @Override
+    public IAxisAngle inverse() {
+        return new AxisAngle(-this.x, -this.y, -this.z, this.angle);
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/math/Quaternion.java

@@ -1,6 +1,6 @@
 package io.github.simplexdev.polarize.math;
 
-import io.github.simplexdev.polarize.api.IQuaternion;
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
 
 public class Quaternion implements IQuaternion {
     private final double w;

Converter/src/main/java/io/github/simplexdev/polarize/math/ScalarTriple.java

@@ -0,0 +1,39 @@
+package io.github.simplexdev.polarize.math;
+
+import io.github.simplexdev.polarize.api.spatial.IVector;
+import io.github.simplexdev.polarize.cartesian.CartesianVector;
+
+public class ScalarTriple {
+    private final double productA;
+    private final double productB;
+    private final double productC;
+
+    private final IVector scalarTripleProduct;
+
+    public ScalarTriple(IVector productA, IVector productB, IVector productC) {
+        this.productA = productA.dot(productB.multiply(productC));
+        this.productB = productB.dot(productC.multiply(productA));
+        this.productC = productC.dot(productA.multiply(productB));
+
+        this.scalarTripleProduct = new CartesianVector(
+                this.productA,
+                this.productB,
+                this.productC);
+    }
+
+    public double getProductA() {
+        return productA;
+    }
+
+    public double getProductB() {
+        return productB;
+    }
+
+    public double getProductC() {
+        return productC;
+    }
+
+    public IVector getScalarTripleProduct() {
+        return scalarTripleProduct;
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/math/function/ArchimedeanSpiral.java

@@ -0,0 +1,36 @@
+package io.github.simplexdev.polarize.math.function;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
+import io.github.simplexdev.polarize.api.units.Point;
+import io.github.simplexdev.polarize.api.units.Theta;
+import io.github.simplexdev.polarize.cartesian.Point2D;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.LinkedHashSet;
+import java.util.Set;
+
+public class ArchimedeanSpiral {
+    private final double origin;
+    private final double step;
+    private final double radius;
+    private final Theta theta;
+
+    public ArchimedeanSpiral(double origin, double step, @NotNull Theta theta) {
+        this.origin = origin;
+        this.step = step;
+        this.theta = theta;
+
+        this.radius = origin + (this.step * theta.getZenith());
+    }
+
+    public Set<IPoint2D> getPoints(IPoint2D start) {
+        Set<IPoint2D> hashSet = new LinkedHashSet<>();
+        hashSet.add(start);
+        for (double i = origin; i < theta.getZenith(); i += step) {
+            double x = radius * Math.cos(i);
+            double z = radius * Math.sin(i);
+            hashSet.add(Point.fromDouble(x + start.getX().get(), z + start.getZ().get()));
+        }
+        return hashSet;
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/math/function/FibonacciLattice.java

@@ -0,0 +1,28 @@
+package io.github.simplexdev.polarize.math.function;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.api.units.Point;
+import io.github.simplexdev.polarize.cartesian.Point3D;
+
+import java.util.LinkedHashSet;
+import java.util.Set;
+
+public final class FibonacciLattice {
+
+    public static Set<IPoint3D> populate(IPoint3D origin, int radius, double step) {
+        Set<IPoint3D> points = new LinkedHashSet<>();
+        final double goldenRatio = (1 + Math.sqrt(5)) / 2;
+
+        for (double i = 0; i <= radius; i += step) {
+            double theta = 2 * Math.PI * i / goldenRatio;
+            double phi = Math.acos(1 - 2 * (i + 0.5) / radius);
+            double x = Math.cos(theta) * Math.sin(phi);
+            double y = Math.cos(phi);
+            double z = Math.sin(theta) * Math.sin(phi);
+
+            points.add(origin.add(Point.fromDouble(x, y, z)));
+        }
+
+        return points;
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/math/function/Integral.java

@@ -0,0 +1,51 @@
+package io.github.simplexdev.polarize.math.function;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.cartesian.Point3D;
+
+import java.util.function.DoubleUnaryOperator;
+import java.util.function.Function;
+import java.util.function.UnaryOperator;
+
+public interface Integral {
+    static double integrate(double lower, double upper, double subIntervals, DoubleUnaryOperator function) {
+        double dx = (upper - lower) / subIntervals;
+        double sum = 0.5 * (function.applyAsDouble(lower) + function.applyAsDouble(upper));
+        for (double i = 1; i < subIntervals; i++) {
+            double s = lower + i * dx;
+            sum += function.applyAsDouble(s);
+        }
+        return dx * sum;
+    }
+
+    static double integrate(IPoint3D origin, IPoint3D destination, double subIntervals, TriFunction<Double, Double, Double, Double> function) {
+        double x1 = origin.getX().get(), x2 = destination.getX().get();
+        double y1 = origin.getY().get(), y2 = destination.getY().get();
+        double z1 = origin.getZ().get(), z2 = destination.getZ().get();
+
+        double dx = (x2 - x1) / subIntervals;
+        double dy = (y2 - y1) / subIntervals;
+        double dz = (z2 - z1) / subIntervals;
+
+        double integral = 0.0;
+
+        for (double i = 0.0; i <= subIntervals; i++) {
+            double x = x1 + i * dx;
+            for (double j = 0.0; j <= subIntervals; j++) {
+                double y = y1 + j * dy;
+                for (double k = 0.0; k <= subIntervals; k++) {
+                    double z = z1 + k * dz;
+                    double weight = 1.0;
+                    if (i == 0.0 || i == subIntervals) weight *= 0.5;
+                    if (j == 0.0 || j == subIntervals) weight *= 0.5;
+                    if (k == 0.0 || k == subIntervals) weight *= 0.5;
+                    integral += weight * function.apply(x, y, z);
+                }
+            }
+        }
+
+        integral *= dx * dy * dz;
+
+        return integral;
+    }
+}

Converter/src/main/java/io/github/simplexdev/polarize/math/function/TriFunction.java

@@ -0,0 +1,6 @@
+package io.github.simplexdev.polarize.math.function;
+
+@FunctionalInterface
+public interface TriFunction<T, S, U, V> {
+    V apply(T t, S s, U u);
+}

Converter/src/main/java/io/github/simplexdev/polarize/polar/Scalar.java

@@ -1,7 +1,7 @@
 package io.github.simplexdev.polarize.polar;
 
-import io.github.simplexdev.polarize.api.IQuaternion;
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
-import io.github.simplexdev.polarize.api.IScalar;
+import io.github.simplexdev.polarize.api.spatial.IScalar;
 
 public class Scalar implements IScalar {
     private final double magnitude;

Converter/src/main/java/io/github/simplexdev/polarize/polar/SphericalUnit.java

@@ -106,7 +106,7 @@ public class SphericalUnit {
      */
     public double adjacent() {
         CartesianUnit unit = Polarizer.toCartesianUnit(this);
-        return unit.getPoint3D().getX();
+        return unit.getPoint3D().getX().get();
     }
 
     /**
@@ -119,6 +119,6 @@ public class SphericalUnit {
      */
     public double opposite() {
         CartesianUnit unit = Polarizer.toCartesianUnit(this);
-        return unit.getPoint3D().getZ();
+        return unit.getPoint3D().getZ().get();
     }
 }

Converter/src/main/java/io/github/simplexdev/polarize/util/Interpolator.java

@@ -1,7 +1,7 @@
 package io.github.simplexdev.polarize.util;
 
-import io.github.simplexdev.polarize.api.IScalar;
+import io.github.simplexdev.polarize.api.spatial.IScalar;
-import io.github.simplexdev.polarize.api.IVector;
+import io.github.simplexdev.polarize.api.spatial.IVector;
 import io.github.simplexdev.polarize.cartesian.CartesianUnit;
 import io.github.simplexdev.polarize.polar.PolarUnit;
 import io.github.simplexdev.polarize.polar.SphericalUnit;

Converter/src/main/java/io/github/simplexdev/polarize/util/Polarizer.java

@@ -1,12 +1,17 @@
 package io.github.simplexdev.polarize.util;
 
-import io.github.simplexdev.polarize.api.IPoint2D;
+import io.github.simplexdev.polarize.api.rotation.IAxisAngle;
-import io.github.simplexdev.polarize.api.IPoint3D;
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
-import io.github.simplexdev.polarize.api.IScalar;
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
-import io.github.simplexdev.polarize.api.IVector;
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.api.spatial.IScalar;
+import io.github.simplexdev.polarize.api.spatial.IVector;
 import io.github.simplexdev.polarize.api.units.Phi;
+import io.github.simplexdev.polarize.api.units.Radius;
 import io.github.simplexdev.polarize.api.units.Theta;
 import io.github.simplexdev.polarize.cartesian.CartesianUnit;
+import io.github.simplexdev.polarize.math.AxisAngle;
+import io.github.simplexdev.polarize.math.Quaternion;
 import io.github.simplexdev.polarize.polar.PolarUnit;
 import io.github.simplexdev.polarize.polar.SphericalUnit;
 
@@ -107,6 +112,16 @@ public class Polarizer {
 
     /**
      * Converts a spherical coordinate (radius, theta, phi) to Cartesian coordinates (x, y, z).
+     * <p>
+     * This method uses the following formula:
+     * <pre>
+     *         {@code radius = sqrt(x^2 + y^2 + z^2)}
+     *         {@code theta = acos(y / radius)}
+     *         {@code phi = atan2(z, x)}
+     *         {@code x = radius * sin(theta) * cos(phi)}
+     *         {@code y = radius * cos(theta)}
+     *         {@code z = radius * sin(theta) * sin(phi)}
+     * </pre>
      *
      * @param radius the radius of the spherical coordinate
      * @param theta  the theta angle in radians of the spherical coordinate
@@ -122,21 +137,22 @@ public class Polarizer {
 
     /**
      * Converts a {@link CartesianUnit} to a {@link PolarUnit}.
+     * This method uses the same formula as {@link #toPolarUnit(double, double)}.
      *
      * @param unit the CartesianUnit to be converted
      * @return a PolarUnit representing the same point as the input CartesianUnit
      */
     public static PolarUnit toPolarUnit(CartesianUnit unit) {
-        double radius = Math.sqrt(
+        double radius = Math.sqrt(unit.getPoint2D().getX().get() * unit.getPoint2D().getX().get() + unit.getPoint2D().getZ().get() * unit.getPoint2D().getZ().get());
-                unit.getPoint2D().getX() * unit.getPoint2D().getX()
+        double theta = Math.atan2(unit.getPoint2D().getX().get(), unit.getPoint2D().getZ().get());
-                        + unit.getPoint2D().getZ() * unit.getPoint2D().getZ());
-        double theta = Math.atan2(unit.getPoint2D().getX(), unit.getPoint2D().getZ());
         return new PolarUnit(radius, theta);
     }
 
     /**
-     * Converts the given {@link CartesianUnit} to a {@link PolarUnit} using the magnitude of the given {@link IVector} as
+     * Converts the given {@link CartesianUnit} to a {@link PolarUnit}.
-     * the radius. The angle theta is calculated from the x and z components of the CartesianUnit using the {@link Math#atan2(double, double)} method.
+     * This method uses the same formula as {@link #toPolarUnit(double, double)},
+     * with the exception that the radius is computed using the given {@link IVector}
+     * instead of the {@link IPoint2D}'s x and z coordinates.
      *
      * @param unit   the {@link CartesianUnit} to convert
      * @param vector the {@link IVector} representing the radius of the resulting {@link PolarUnit}
@@ -144,12 +160,14 @@ public class Polarizer {
      */
     public static PolarUnit toPolarUnit(CartesianUnit unit, IVector vector) {
         double radius = vector.length();
-        double theta = Math.atan2(unit.getPoint2D().getX(), unit.getPoint2D().getZ());
+        double theta = Math.atan2(unit.getPoint2D().getX().get(), unit.getPoint2D().getZ().get());
         return new PolarUnit(radius, theta);
     }
 
     /**
      * Returns a {@link PolarUnit} representing the polar coordinates of the given 2D point in relation to the given vector.
+     * <p>
+     * This method uses the same formula as {@link #toPolarUnit(double, double)}.
      *
      * @param point  the point to convert to polar coordinates
      * @param vector the vector used as a reference for the polar coordinates
@@ -157,16 +175,25 @@ public class Polarizer {
      */
     public static PolarUnit toPolarUnit(IPoint2D point, IVector vector) {
         double radius = vector.length();
-        double theta = Math.atan2(point.getX(), point.getZ());
+        double theta = Math.atan2(point.getX().get(), point.getZ().get());
         return new PolarUnit(radius, theta);
     }
 
     /**
      * Converts a 2D point in Cartesian coordinates to a polar unit.
+     * <p>
+     * The conversion is based on the following formula:
+     * <pre>
+     *          {@code radius = sqrt(x^2 + z^2)}
+     *          {@code theta = atan2(x, z)}
+     *             where:
+     *         x = {@link IPoint2D#getX()}
+     *         z = {@link IPoint2D#getZ()}
+     * </pre>
      *
      * @param x the x-coordinate of the point
      * @param z the z-coordinate of the point
-     * @return a {@code PolarUnit} representing the polar coordinates of the point
+     * @return a {@link PolarUnit} representing the polar coordinates of the point
      */
     public static PolarUnit toPolarUnit(double x, double z) {
         double radius = Math.sqrt(x * x + z * z);
@@ -175,23 +202,36 @@ public class Polarizer {
     }
 
     /**
-     * Converts a CartesianUnit to a SphericalUnit.
+     * Converts a {@link CartesianUnit} to a {@link SphericalUnit}.
+     * <p>
+     * The radius is calculated by creating a new vector based on the CartesianUnit's
+     * x, y, and z coordinates, then using {@link IVector#length()} to acquire the {@link IScalar}.
+     * <p>
+     * The angles are then calculated from {@link IScalar#getMagnitude()}.
+     * <p>
+     * This method uses the same formula as {@link #toSphericalUnit(double, double, double)}.
      *
      * @param unit the CartesianUnit to be converted.
      * @return the SphericalUnit representing the same point as the input CartesianUnit.
      */
     public static SphericalUnit toSphericalUnit(CartesianUnit unit) {
-        double radius = Math.sqrt(
+        double radius = Math.sqrt(unit.getPoint3D().getX().get()
-                unit.getPoint3D().getX() * unit.getPoint3D().getX()
+                * unit.getPoint3D().getX().get()
-                        + unit.getPoint3D().getY() * unit.getPoint3D().getY()
+                + unit.getPoint3D().getY().get()
-                        + unit.getPoint3D().getZ() * unit.getPoint3D().getZ());
+                * unit.getPoint3D().getY().get()
-        double theta = Math.acos(unit.getPoint3D().getY() / radius);
+                + unit.getPoint3D().getZ().get()
-        double phi = Math.atan2(unit.getPoint3D().getX(), unit.getPoint3D().getZ());
+                * unit.getPoint3D().getZ().get());
+        double theta = Math.acos(unit.getPoint3D().getY().get()
+                / radius);
+        double phi = Math.atan2(unit.getPoint3D().getX().get(),
+                unit.getPoint3D().getZ().get());
         return new SphericalUnit(radius, theta, phi);
     }
 
     /**
      * Converts the specified {@link IPoint3D} to a {@link SphericalUnit} using the specified {@link IVector}.
+     * <p>
+     * This method uses the same formula as {@link #toSphericalUnit(double, double, double)}
      *
      * @param point  the point to convert to a spherical unit
      * @param vector the vector to use for the conversion
@@ -199,18 +239,33 @@ public class Polarizer {
      */
     public static SphericalUnit toSphericalUnit(IPoint3D point, IVector vector) {
         double radius = vector.length();
-        double theta = Math.acos(point.getY() / radius);
+        double theta = Math.acos(point.getY().get() / radius);
-        double phi = Math.atan2(point.getX(), point.getZ());
+        double phi = Math.atan2(point.getX().get(), point.getZ().get());
         return new SphericalUnit(radius, theta, phi);
     }
 
     /**
      * Converts the given Cartesian coordinates (x, y, z) to spherical coordinates (radius, theta, phi).
+     * <p>
+     * The conversion is based on the following formula:
+     * <pre>
+     *         {@code radius = sqrt(x^2 + y^2 + z^2)}
+     *         {@code theta = acos(y / radius)}
+     *         {@code phi = atan2(x, z)}
+     *             where:
+     *         {@code radius} is the {@link Radius} (scalar) of the spherical coordinate
+     *         {@code theta} is the {@link Theta} angle (zenith) in radians of the spherical coordinate
+     *         {@code phi} is the {@link Phi} angle (azimuth) in radians of the spherical coordinate
+     * </pre>
+     * <p>
+     * The resulting spherical coordinates are returned as a new {@link SphericalUnit}.
+     * <p>
+     * The returned {@link SphericalUnit} is guaranteed to reflect the same coordinates as the input.
      *
      * @param x the x-coordinate
      * @param y the y-coordinate
      * @param z the z-coordinate
-     * @return a new {@code SphericalUnit} representing the converted spherical coordinates
+     * @return a new {@link SphericalUnit} representing the converted spherical coordinates
      */
     public static SphericalUnit toSphericalUnit(double x, double y, double z) {
         double radius = Math.sqrt(x * x + y * y + z * z);
@@ -218,4 +273,70 @@ public class Polarizer {
         double phi = Math.atan2(x, z);
         return new SphericalUnit(radius, theta, phi);
     }
+
+    /**
+     * Converts the given {@link IQuaternion} to an {@link IAxisAngle}.
+     * <p>
+     * The conversion is based on the following formula:
+     * <pre>
+     *          {@code r = (x * sin(angle/2), y * sin(angle/2), z * sin(angle/2), cos(angle/2))}
+     *              where:
+     *         sin = {@link Math#sin(double)},
+     *         cos = {@link Math#cos(double)},
+     *         x = {@link IQuaternion#getX()},
+     *         y = {@link IQuaternion#getY()},
+     *         z = {@link IQuaternion#getZ()}
+     *         angle = {@link IQuaternion#getW()}
+     *         r = {@link IAxisAngle}
+     * </pre>
+     *
+     * @param quaternion the {@link IQuaternion} to convert
+     * @return a new {@link IAxisAngle} representing the converted {@link IQuaternion}
+     */
+    public static IAxisAngle toAxisAngle(IQuaternion quaternion) {
+        double angle = 2 * Math.acos(quaternion.getW());
+        double s = Math.sqrt(1 - quaternion.getW() * quaternion.getW());
+
+        double x, y, z;
+
+        if (s < 0.001) {
+            x = quaternion.getX();
+            y = quaternion.getY();
+            z = quaternion.getZ();
+        } else {
+            x = quaternion.getX() / s;
+            y = quaternion.getY() / s;
+            z = quaternion.getZ() / s;
+        }
+        return new AxisAngle(x, y, z, () -> angle);
+    }
+
+    /**
+     * Converts the given {@link IAxisAngle} to a {@link IQuaternion}.
+     * <p>
+     * The conversion is based on the following formula:
+     * <pre>
+     *          {@code q = (x * sin(angle / 2), y * sin(angle / 2), z * sin(angle / 2), cos(angle / 2))}
+     *              where:
+     *         sin = {@link Math#sin(double)}
+     *         cos = {@link Math#cos(double)}
+     *         angle = {@link Theta#getZenith()}
+     *         x = {@link IAxisAngle#getX()}
+     *         y = {@link IAxisAngle#getY()}
+     *         z = {@link IAxisAngle#getZ()}
+     *         q = the resulting quaternion.
+     * </pre>
+     *
+     * @param axisAngle the {@link IAxisAngle} to convert
+     * @return a {@link IQuaternion} representing the same rotation as the given {@link IAxisAngle}
+     */
+    public IQuaternion toQuaternion(IAxisAngle axisAngle) {
+        double angle = axisAngle.getAngle().getZenith();
+        double x = axisAngle.getX();
+        double y = axisAngle.getY();
+        double z = axisAngle.getZ();
+        double w = Math.cos(angle / 2);
+        double s = Math.sin(angle / 2);
+        return new Quaternion(x * s, y * s, z * s, w);
+    }
 }

Converter/src/main/java/io/github/simplexdev/polarize/util/Rotator.java

@@ -1,10 +1,11 @@
 package io.github.simplexdev.polarize.util;
 
-import io.github.simplexdev.polarize.api.IPoint2D;
+import io.github.simplexdev.polarize.api.rotation.IQuaternion;
-import io.github.simplexdev.polarize.api.IPoint3D;
+import io.github.simplexdev.polarize.api.spatial.IPoint2D;
-import io.github.simplexdev.polarize.api.IQuaternion;
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
-import io.github.simplexdev.polarize.math.Point2D;
+import io.github.simplexdev.polarize.api.units.Point;
-import io.github.simplexdev.polarize.math.Point3D;
+import io.github.simplexdev.polarize.cartesian.Point2D;
+import io.github.simplexdev.polarize.cartesian.Point3D;
 import io.github.simplexdev.polarize.math.Quaternion;
 import io.github.simplexdev.polarize.polar.Delta;
 import io.github.simplexdev.polarize.polar.PolarUnit;
@@ -35,11 +36,13 @@ public class Rotator {
      * @return the rotated point.
      */
     public static IPoint3D rotateX(IPoint3D point, SphericalUnit unit) {
-        double x = point.getX();
+        double x = point.getX().get();
-        double y = point.getY() * Math.cos(unit.theta()) - point.getZ() * Math.sin(unit.theta());
+        double y = point.getY().multiply(Math.cos(unit.theta()))
-        double z = point.getY() * Math.sin(unit.theta()) + point.getZ() * Math.cos(unit.theta());
+                - point.getZ().multiply(Math.sin(unit.theta()));
+        double z = point.getY().multiply(Math.sin(unit.theta()))
+                + point.getZ().multiply(Math.cos(unit.theta()));
 
-        return new Point3D(x, y, z);
+        return Point.fromDouble(x, y, z);
     }
 
     /**
@@ -52,11 +55,13 @@ public class Rotator {
      * @return the rotated point.
      */
     public static IPoint3D rotateY(IPoint3D point, SphericalUnit unit) {
-        double x = point.getX() * Math.cos(unit.phi()) - point.getZ() * Math.sin(unit.phi());
+        double x = point.getX().multiply(Math.cos(unit.phi()))
-        double y = point.getY();
+                - point.getZ().multiply(Math.sin(unit.phi()));
-        double z = point.getX() * Math.sin(unit.phi()) + point.getZ() * Math.cos(unit.phi());
+        double y = point.getY().get();
+        double z = point.getX().multiply(Math.sin(unit.phi()))
+                + point.getZ().multiply(Math.cos(unit.phi()));
 
-        return new Point3D(x, y, z);
+        return Point.fromDouble(x, y, z);
     }
 
     /**
@@ -65,15 +70,17 @@ public class Rotator {
      * This will rotate the point around the z-axis.
      *
      * @param point the point to rotate.
-     * @param unit the spherical unit to rotate the point with.
+     * @param unit  the spherical unit to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint3D rotateZ(IPoint3D point, SphericalUnit unit) {
-        double x = point.getX() * Math.cos(unit.theta()) - point.getY() * Math.sin(unit.theta());
+        double x = point.getX().multiply(Math.cos(unit.theta()))
-        double y = point.getX() * Math.sin(unit.theta()) + point.getY() * Math.cos(unit.theta());
+                - point.getY().multiply(Math.sin(unit.theta()));
-        double z = point.getZ();
+        double y = point.getX().multiply(Math.sin(unit.theta()))
+                + point.getY().multiply(Math.cos(unit.theta()));
+        double z = point.getZ().get();
 
-        return new Point3D(x, y, z);
+        return Point.fromDouble(x, y, z);
     }
 
     /**
@@ -83,19 +90,19 @@ public class Rotator {
      *
      * @param point the point to rotate.
      * @param delta the delta values to rotate the point with.
-     * @param unit the spherical unit to rotate the point with.
+     * @param unit  the spherical unit to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint3D fullRotation(IPoint3D point, Delta delta, SphericalUnit unit) {
         double r = unit.radius() * Math.cos(unit.theta() + delta.theta()) * Math.cos(unit.phi() + delta.phi());
-        double theta = Math.atan2(point.getX(), point.getZ()) + delta.theta();
+        double theta = Math.atan2(point.getX().get(), point.getZ().get()) + delta.theta();
-        double phi = Math.atan2(Utilities.magnitudeOf(point.getX(), point.getZ()), point.getY()) + delta.phi();
+        double phi = Math.atan2(Utilities.magnitudeOf(point.getX().get(), point.getZ().get()), point.getY().get()) + delta.phi();
 
         double xRot = r * Math.sin(theta) * Math.cos(phi);
         double yRot = r * Math.cos(theta);
         double zRot = r * Math.sin(theta) * Math.sin(phi);
 
-        return new Point3D(xRot, yRot, zRot);
+        return Point.fromDouble(xRot, yRot, zRot);
     }
 
     /**
@@ -104,13 +111,15 @@ public class Rotator {
      * This will rotate the point around the x-axis.
      *
      * @param point the point to rotate.
-     * @param unit the polar unit to rotate the point with.
+     * @param unit  the polar unit to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint2D rotateX(IPoint2D point, PolarUnit unit) {
-        double x = point.getZ() * Math.cos(unit.theta()) - point.getX() * Math.sin(unit.theta());
+        double x = point.getZ().multiply(Math.cos(unit.theta()))
-        double z = point.getZ() * Math.sin(unit.theta()) + point.getX() * Math.cos(unit.theta());
+                - point.getX().multiply(Math.sin(unit.theta()));
-        return new Point2D(x, z);
+        double z = point.getZ().multiply(Math.sin(unit.theta()))
+                + point.getX().multiply(Math.cos(unit.theta()));
+        return Point.fromDouble(x, z);
     }
 
     /**
@@ -119,13 +128,15 @@ public class Rotator {
      * This will rotate the point around the y-axis.
      *
      * @param point the point to rotate.
-     * @param unit the polar unit to rotate the point with.
+     * @param unit  the polar unit to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint2D rotateZ(IPoint2D point, PolarUnit unit) {
-        double x = point.getX() * Math.cos(unit.theta()) - point.getZ() * Math.sin(unit.theta());
+        double x = point.getX().multiply(Math.cos(unit.theta()))
-        double z = point.getX() * Math.sin(unit.theta()) + point.getZ() * Math.cos(unit.theta());
+                - point.getZ().multiply(Math.sin(unit.theta()));
-        return new Point2D(x, z);
+        double z = point.getX().multiply(Math.sin(unit.theta()))
+                + point.getZ().multiply(Math.cos(unit.theta()));
+        return Point.fromDouble(x, z);
     }
 
     /**
@@ -134,48 +145,50 @@ public class Rotator {
      * This will rotate the point around the x-axis and z-axis.
      *
      * @param point the point to rotate.
-     * @param unit the polar unit to rotate the point with.
+     * @param unit  the polar unit to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint2D fullRotation(IPoint2D point, SphericalUnit unit) {
-        double x = point.getX() * Math.cos(unit.theta()) - point.getZ() * Math.sin(unit.theta());
+        double x = point.getX().multiply(Math.cos(unit.theta()))
-        double z = point.getX() * Math.sin(unit.theta()) + point.getZ() * Math.cos(unit.theta());
+                - point.getZ().multiply(Math.sin(unit.theta()));
-        return new Point2D(x, z);
+        double z = point.getX().multiply(Math.sin(unit.theta()))
+                + point.getZ().multiply(Math.cos(unit.theta()));
+        return Point.fromDouble(x, z);
     }
 
     /**
      * Rotates a point in 3d space using a quaternion.
      * The returned result is a point in 3d space represented by {@link IPoint3D}.
      *
-     * @param point the point to rotate.
+     * @param point      the point to rotate.
      * @param quaternion the quaternion to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint3D rotate(IPoint3D point, IQuaternion quaternion) {
-        IQuaternion pQuat = new Quaternion(0.0, point.getX(), point.getY(), point.getZ());
+        IQuaternion pQuat = new Quaternion(0.0, point.getX().get(), point.getY().get(), point.getZ().get());
 
         IQuaternion conjugate = quaternion.conjugate();
 
         IQuaternion w = conjugate.multiply(pQuat).multiply(quaternion);
 
-        return new Point3D(w.getX(), w.getY(), w.getZ());
+        return Point.fromDouble(w.getX(), w.getY(), w.getZ());
     }
 
     /**
      * Rotates a point in 2d space using a quaternion.
      * The returned result is a point in 2d space represented by {@link IPoint2D}.
      *
-     * @param point the point to rotate.
+     * @param point      the point to rotate.
      * @param quaternion the quaternion to rotate the point with.
      * @return the rotated point.
      */
     public static IPoint2D rotate(IPoint2D point, IQuaternion quaternion) {
-        IQuaternion pQuat = new Quaternion(0.0, point.getX(), 0.0, point.getZ());
+        IQuaternion pQuat = new Quaternion(0.0, point.getX().get(), 0.0, point.getZ().get());
 
         IQuaternion conjugate = quaternion.conjugate();
 
         IQuaternion w = conjugate.multiply(pQuat).multiply(quaternion);
 
-        return new Point2D(w.getX(), w.getZ());
+        return Point.fromDouble(w.getX(), w.getZ());
     }
 }

Converter/src/main/java/io/github/simplexdev/polarize/util/Utilities.java

@@ -26,6 +26,7 @@ public class Utilities {
      * This represents 360 degrees in radians.
      */
     public static final double RADIAN_360 = Math.PI * 2;
+
     private Utilities() {
         throw new AssertionError();
     }

Converter/src/test/java/io/github/simplexdev/polarize/math/FibonacciLatticeTest.java

@@ -0,0 +1,23 @@
+package io.github.simplexdev.polarize.math;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import io.github.simplexdev.polarize.api.spatial.IPoint3D;
+import io.github.simplexdev.polarize.cartesian.Point3D;
+import io.github.simplexdev.polarize.log.PolarizeLogger;
+import io.github.simplexdev.polarize.math.function.FibonacciLattice;
+import org.junit.jupiter.api.Test;
+
+class FibonacciLatticeTest
+{
+    /**
+     * Method under test: {@link FibonacciLattice#populate(IPoint3D, int, double)}
+     */
+    @Test
+    void testDisplayPoints()
+    {
+        FibonacciLattice.populate(new Point3D(10,15,5), 10, 0.1)
+                .forEach(point -> PolarizeLogger.info("X: " + point.getX() + " Y: " + point.getY() + " Z: " + point.getZ()));
+    }
+}
+

Converter/src/test/java/io/github/simplexdev/polarize/math/Point3DTest.java

@@ -0,0 +1,20 @@
+package io.github.simplexdev.polarize.math;
+
+import io.github.simplexdev.polarize.cartesian.Point3D;
+import org.junit.jupiter.api.Test;
+
+class Point3DTest
+{
+    /**
+     * Method under test: {@link Point3D#drawLineTestMethod()}
+     */
+    @Test
+    void testDrawLineTestMethod()
+    {
+        // TODO: Complete this test.
+        //   Diffblue AI was unable to find a test
+
+        (new Point3D(2.0d, 3.0d, 10.0d)).drawLineTestMethod();
+    }
+}
+

build.gradle

@@ -20,7 +20,7 @@ subprojects {
 }
 
 tasks.build {
-    dependsOn(":Commons:build", ":Paper:build")
+    dependsOn(":Converter:build", ":Bukkit:build")
 }
 
 test {

settings.gradle

@@ -1,4 +1,6 @@
 rootProject.name = 'Polarize'
-include 'Commons'
+include 'Converter'
-include 'Paper'
+include 'Bukkit'
+include 'Caravan'
+include 'Caravan'