LeetCode 1037: Valid Boomerang
A clear explanation of checking if three points form a boomerang (non-collinear) using the cross product.
Tag
Geometry
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LeetCode 883: Projection Area of 3D Shapes
A clear explanation of computing the projection areas of stacked cubes from top, front, and side views.
LeetCode 612: Shortest Distance in a Plane
A SQL guide for finding the minimum Euclidean distance between any two points in a 2D plane.
LeetCode 218: The Skyline Problem
A clear explanation of computing the skyline formed by buildings using sweep line and a max-heap.
LeetCode 149: Max Points on a Line
Find the maximum number of points lying on the same straight line using slope counting and normalization.
LeetCode 963: Minimum Area Rectangle II
A clear explanation of finding the minimum-area rectangle from points when the rectangle may be rotated.
LeetCode 836: Rectangle Overlap
A clear explanation of the Rectangle Overlap problem using axis projections and positive intersection area.
LeetCode 892: Surface Area of 3D Shapes
A clear explanation of computing the exposed surface area of stacked cubes by adding tower area and subtracting shared faces.
LeetCode 858: Mirror Reflection
A clear explanation of Mirror Reflection using room unfolding, least common multiples, and parity.
LeetCode 939: Minimum Area Rectangle
A clear explanation of solving Minimum Area Rectangle using diagonal point pairs and constant-time point lookup.
LeetCode 812: Largest Triangle Area
A geometry solution for finding the largest triangle area by checking every triplet of points with the cross product formula.
LeetCode 789: Escape The Ghosts
A clear explanation of deciding whether escape is possible by comparing Manhattan distances to the target.
LeetCode 711: Number of Distinct Islands II
A clear explanation of counting distinct island shapes under rotation and reflection using normalization and geometric transformations.
LeetCode 593: Valid Square
A clear geometry solution for checking whether four unordered points form a valid square.
LeetCode 587: Erect the Fence
A clear convex hull solution for returning all trees that lie on the fence boundary.
LeetCode 497: Random Point in Non-overlapping Rectangles
A clear explanation of uniformly picking an integer point from non-overlapping rectangles using prefix sums and binary search.
LeetCode 478: Generate Random Point in a Circle
A clear explanation of generating uniformly random points inside a circle using polar coordinates.
LeetCode 469: Convex Polygon
A clear explanation of checking whether ordered points form a convex polygon using cross products.
LeetCode 447: Number of Boomerangs
Count ordered boomerang tuples by fixing each point as the center and grouping other points by squared distance.
LeetCode 391: Perfect Rectangle
A clear explanation of checking whether many small axis-aligned rectangles form one exact rectangular cover using area and corner parity.
LeetCode 356: Line Reflection
A clear explanation of checking whether 2D points are symmetric around a vertical line using min and max x-coordinates.
LeetCode 335: Self Crossing
A clear explanation of Self Crossing using constant-space checks for the only possible crossing patterns.
LeetCode 223: Rectangle Area
A clear explanation of computing the total covered area of two axis-aligned rectangles by subtracting their overlap.
3.4 Geometric Data Structures
KD-trees, R-trees, quadtrees, octrees, Delaunay triangulation, Voronoi diagrams, HNSW, range trees, and sweep line structures.
k-d Tree Search
Search for nearest or range points in k-dimensional space using recursive axis splitting.
Range Tree Search
Search for all points within a multidimensional range using layered balanced search trees.
4.5 Examples Across Algebra and Geometry
Examples of first order structures from algebra, order theory, graph theory, and geometry.
53. Differential Geometry
This volume studies smooth geometric structures using calculus.
52. Convex and Discrete Geometry
This volume studies convex sets, polytopes, and discrete geometric structures.
51. Geometry
This volume studies geometric structures, transformations, and invariants.