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计算机图形
12
engines
Cubic Bézier curve
Cubic Bézier curve
三次 B(t)=(1−t)³P0+…+t³P3 · de Casteljau · 控制多边形
B(t)=(1−t)³P₀+3(1−t)²t·P₁+3(1−t)t²·P₂+t³P₃ · drag the control points
Catmull-Rom spline
Catmull-Rom spline
过控制点插值 · 切线由相邻点 · C1 连续 · vs 贝塞尔
An interpolating cubic spline that threads through every control point · drag to reshape
Perlin noise (coherent noise)
Perlin noise (coherent noise)
梯度插值相干噪声 · 频率/振幅/八度分形 · 种子确定
Smooth seeded lattice noise · fractal octaves (fBm) · deterministic, no randomness
Homogeneous coordinates · affine transforms
Homogeneous coordinates · affine transforms
3×3 平移/旋转/缩放/剪切 · 复合=矩阵相乘 · 不可交换
A 3×3 matrix per transform; composing = matrix multiply, and order does not commute
Quaternions · 3D rotation
Quaternions · 3D rotation
q=(cos(θ/2),sin(θ/2)·n̂) · q·v·q⁻¹ · 避免万向锁
A unit quaternion q = (cos(θ/2), sin(θ/2)·n̂) rotates a vector without gimbal lock
Barycentric coordinates · triangle interpolation
Barycentric coordinates · triangle interpolation
P=αA+βB+γC · α+β+γ=1 · 内外判定 · 属性插值
P = α·A + β·B + γ·C with α + β + γ = 1; all three ≥ 0 ⇔ P is inside
Bresenham's line algorithm
Bresenham's line algorithm
整数增量 · 误差项决定步进 · 栅格阶梯 · 无浮点
Integer-only rasterization of a straight line · exact staircase
Scanline polygon fill
Scanline polygon fill
逐扫描线求交 · 配对 · 奇偶规则 · 凹多边形
Even-odd rule fills a concave polygon span by span
Z-buffer hidden-surface removal
Z-buffer hidden-surface removal
逐像素最近深度 · 近覆盖远 · 消隐 · 与绘制顺序无关
Nearest depth wins each pixel — independent of draw order
Ray–triangle intersection (Möller–Trumbore)
Ray–triangle intersection (Möller–Trumbore)
Möller-Trumbore · t/u/v 重心 · 命中判定 · 平行
Solve for t and the barycentric (u,v); the ray hits iff u≥0, v≥0, u+v≤1, t>0
Phong reflection model
Phong reflection model
I=ka+kd(N·L)+ks(R·V)ⁿ · 环境/漫反射/镜面高光
I = ka·ambient + kd·(N·L)·diffuse + ks·(R·V)^shininess·specular
HSV color space (HSV ↔ RGB)
HSV color space (HSV ↔ RGB)
色相/饱和度/明度 ↔ RGB · 色相环 · 往返转换
Chroma C = V·S, X = C·(1−|(H/60 mod 2)−1|), m = V−C, sector-based assignment