AS WJEC Art: Formula & Theorem Quick Reference Guide | AS WJEC 艺术：公式定理速查手册

📚 AS WJEC Art: Formula & Theorem Quick Reference Guide | AS WJEC 艺术：公式定理速查手册

In AS Level Art and Design, creative practice is supported by a set of fundamental principles that operate much like formulas in science. These visual ‘theorems’ – colour mixing, perspective construction, compositional ratios – provide reliable frameworks for building compelling artworks. This guide distils the essential rules and mathematical relationships you need to apply with confidence in your WJEC portfolio, from the physics of light to the geometry of balance.

在 AS 艺术与设计课程中，创作实践由一套类似于科学公式的基本原理支撑。这些视觉“定理” —— 色彩混合、透视构建、构图比例 —— 为创作引人注目的作品提供了可靠的框架。本手册提炼了 WJEC 作品集中需要自信运用的基本规则和数学关系，从光的物理特性到平衡的几何学。

1. Colour Primaries & Secondaries | 色彩原色与间色

All colour mixing can be traced to the primary triad. In subtractive mixing (pigment, paint) the primaries are cyan, magenta and yellow. When any two are mixed in equal parts, they produce secondary hues: Cyan + Magenta → Blue-Violet, Magenta + Yellow → Red-Orange, Yellow + Cyan → Green. This is the artist’s colour wheel formula.

所有色彩混合都可追溯到三原色。在减色混合（颜料、绘画）中，原色是青、品红和黄。任意两种等量混合都会产生间色：青 + 品红 → 蓝紫色，品红 + 黄 → 红橙色，黄 + 青 → 绿色。这就是艺术家的色轮公式。

Primary triad (subtractive): C + M + Y. Cyan + Magenta = Blue-Violet, Magenta + Yellow = Red-Orange, Yellow + Cyan = Green.

减色三原色：青 + 品红 + 黄。青 + 品红 = 蓝紫，品红 + 黄 = 红橙，黄 + 青 = 绿。
In light (additive, screen), primaries are Red, Green, Blue. R + G = Yellow, G + B = Cyan, R + B = Magenta.

在光（加色，屏幕）中，原色是红、绿、蓝。红 + 绿 = 黄，绿 + 蓝 = 青，红 + 蓝 = 品红。

2. Complementary Contrast & Harmonies | 互补对比与和谐

Complementary pairs sit exactly opposite on the colour wheel and create maximum contrast. The classic pairs derived from the artist’s wheel are: Red ↔ Green, Blue ↔ Orange, Yellow ↔ Purple. Mixing complements neutralises intensity (Red + Green → earthy brown). This formula is central to colour theory balance.

互补色对在色轮上正相对，产生最大对比。源自艺术家色轮的经典互补对为：红 ↔ 绿，蓝 ↔ 橙，黄 ↔ 紫。混合互补色会中和饱和度（红 + 绿 → 土棕色）。这一公式是色彩理论平衡的核心。

For harmonious schemes, use split-complements (one hue + the two colours adjacent to its complement), triadic (three evenly spaced hues, e.g. Red, Yellow, Blue) or analogous groups (three neighbours on the wheel, e.g. Yellow-Green, Yellow, Yellow-Orange). Each scheme follows a geometric interval formula on the wheel.

要创造和谐配色，可使用分裂互补色（一个色相 + 其互补色相邻的两色）、三色组（均匀分布的三个色相，如红、黄、蓝）或类似色组（色轮上相邻三色，如黄绿、黄、黄橙）。每种方案都遵循色轮上的几何间隔公式。

3. Value, Saturation & Intensity Formula | 明度、饱和度与强度公式

Colour is described by three dimensions: Hue (the colour family), Value (lightness/darkness) and Saturation (purity/greyness). Adding white to a hue raises value and reduces saturation, creating a tint. Adding black reduces value, producing a shade. Adding grey (equal black + white) reduces saturation without major value shift, forming a tone.

色彩由三个维度描述：色相（色彩家族）、明度（亮暗）和饱和度（纯度/灰度）。将白色加入色相会提高明度、降低饱和度，产生浅色调（tint）。加入黑色会降低明度，产生暗色调（shade）。加入灰色（等量黑+白）会在不明显改变明度的情况下降低饱和度，形成中间色调（tone）。

Luminosity contrast can be expressed as a ratio: the higher the value contrast between figure and ground, the more immediate the visual impact. Maximum readability occurs at a value difference of > 50%.

明度对比可用比率表示：主体与背景之间的明度对比越高，视觉冲击力越强。当明度差异超过 50% 时，可读性最强。

4. One-Point Perspective Formula | 一点透视公式

In one-point perspective, all parallel lines receding into the distance converge at a single vanishing point (VP) on the horizon line (eye level). The formula: VP lies directly opposite the viewer’s central line of sight. All verticals remain vertical; all horizontals parallel to the picture plane remain horizontal. Depth is scaled using orthogonal lines radiating from VP.

在一点透视中，所有向远方后退的平行线都汇聚于地平线（目高）上的一个消失点。公式：消失点正对观者中心视线。所有垂直线保持垂直；所有与画面平行的水平线保持水平。深度通过从消失点放射出的正交线来尺度化。

A standard spacing formula for recession: if the first segment depth is ‘d’, each subsequent equal segment in perspective is calculated by drawing diagonals through the midpoint of the previous unit. This ensures mathematically consistent foreshortening.

后退的标准间距公式：如果第一段深度为“d”，那么透视中每个后续等段都通过前一单元的中点画对角线来计算。这确保了符合数学规律的前缩。

Horizon Line = Eye Level

地平线 = 视平线

VP on HL

消失点在地平线上

Orthogonals meet at VP

正交线交于消失点

Verticals remain vertical

垂线保持垂直

5. Two-Point Perspective Rule | 两点透视法则

When an object is rotated so that its vertical edges still run parallel to the picture plane, but horizontal edges recede, two vanishing points are placed on the horizon line. Left VP (VPL) and Right VP (VPR). All parallel horizontal edges on one side converge to VPL, the other side to VPR. The formula for the distance between VPs depends on the angle of rotation; a common classroom approximation sets VPL and VPR at distances equal to the width of the object plus viewer distance.

当物体旋转，使其垂直边仍与画面平行，而水平边后退时，地平线上会出现两个消失点：左消失点（VPL）和右消失点（VPR）。一侧的所有平行水平边汇聚至 VPL，另一侧至 VPR。两消失点之间的距离公式取决于旋转角度；课堂常用近似法将 VPL 和 VPR 分别设在距物体宽度加上观者距离的位置。

The station point (SP) determines cone of vision: to avoid distortion, keep objects within a 60° cone, where the distance from SP to the picture plane is approximately the width of the scene. Severe objects outside this cone appear stretched.

站点（SP）决定视野锥角：为避免变形，物体应保持在 60° 锥角内，此时站点到画面的距离约等于场景宽度。锥角外的物体会显得拉伸。

6. Aerial Perspective & Attenuation | 空气透视与衰减

Aerial perspective mimics atmospheric effects on colour and detail. As objects recede, they lose contrast, shift towards blue-grey (cooler), and edges soften. A practical attenuation formula: for every doubling of distance, saturation drops by about 50% and value lightens towards the sky’s tone. This principle is essential for landscape depth without linear convergence.

空气透视模仿大气对色彩和细节的影响。随着物体后退，它们的对比度下降，色调偏蓝灰（变冷），边缘模糊。实用的衰减公式：距离每增加一倍，饱和度大约下降 50%，明度向天空的色调变亮。这一原理对于无需线性汇聚来表现风景深度至关重要。

7. Golden Ratio (φ) in Composition | 构图中的黄金比例 (φ)

The golden ratio, denoted by the Greek letter phi (φ), is approximately 1.618 : 1. In a line segment, if the whole length (a+b) is to the larger part (a) as the larger part is to the smaller (b): (a+b)/a = a/b = φ. In visual composition, placing the focal point at a golden ratio division of the picture plane creates a naturally balanced division. The proportion is often used to decide the horizon placement: either at the upper golden section (≈61.8% from bottom) or lower golden section (≈38.2% from bottom).

黄金比例，用希腊字母 φ 表示，约为 1.618:1。在线段中，如果全长 (a+b) 与较大部分 (a) 之比等于较大部分与较小部分 (b) 之比：(a+b)/a = a/b = φ。在视觉构图中，将焦点放在画面的黄金分割点处会创造出自然平衡的分割。该比例常用于确定地平线位置：放在上方黄金分割（距底部约 61.8%）或下方黄金分割（距底部约 38.2%）处。

The golden rectangle, where the ratio of long side to short side equals φ, can be subdivided into a square and a smaller golden rectangle infinitely. Many classical artworks follow this underlying grid.

黄金矩形（长边与短边之比等于 φ）可无限细分出一个正方形和一个更小的黄金矩形。许多古典艺术作品都遵循这一潜在网格。

8. Rule of Thirds & Dynamic Symmetry | 三分法则与动态对称

A practical simplification of the golden ratio is the rule of thirds: divide the frame into a 3×3 grid. Placing key elements along the lines or at the intersections (power points) creates tension and interest. Each intersection is at (33.3%, 66.6%) of the width and height, offering a close approximation to φ’s 38.2%/61.8% divisions.

黄金比例的实用简化是三分法则：将画面分成 3×3 网格。将关键元素放置于线上或交叉点（兴趣点）可以产生张力和趣味。每个交叉点位于宽度和高度的 33.3% 和 66.6% 处，与 φ 的 38.2%/61.8% 分割点非常近似。

Dynamic symmetry expands this by using root rectangles (√2, √3, √4, √5) derived from the square’s diagonal. The √2 rectangle, for instance, has a side ratio 1 : √2 (≈1 : 1.414), and when folded in half, maintains the same proportion. This underlies standard paper sizes (A4, A3) and is a natural compositional grid.

动态对称通过使用从正方形对角线导出的根号矩形（√2, √3, √4, √5）对此加以扩展。例如，√2 矩形的边长比为 1 : √2（≈1 : 1.414），对折后仍保持相同比例。这是标准纸张尺寸（A4、A3）的基础，也是一种天然的构图网格。

9. Compositional Balance: Visual Weight Equation | 构图平衡：视觉重量方程

Balance is achieved when the visual weights on either side of an axis feel equivalent. A simplified visual weight formula considers: W = S × C × P, where S = size (area), C = contrast (value and colour intensity), P = position (distance from centre, leverage). A small, highly contrasting shape near the edge can balance a large, low-contrast mass near the centre.

当轴线两侧的视觉重量感觉相等时即获得平衡。简化的视觉重量公式为：W = S × C × P，其中 S = 尺寸（面积），C = 对比度（明度和色彩强度），P = 位置（距中心的距离，杠杆作用）。边缘处一个高对比度的小形状可以平衡中心附近一个低对比度的大块。

Symmetrical balance: mirror weights about a central axis.

对称平衡：围绕中轴线镜像重量。
Asymmetrical balance: different elements with equal calculated weight.

非对称平衡：计算重量相等的不同元素。
Radial balance: weights radiating from a central point.

放射平衡：重量从中点向外辐射。

10. Light Logic: Shadow Construction | 光影逻辑：阴影构建

The behaviour of light on form follows predictable geometry. A cast shadow is created where an object blocks light; its edge is determined by rays from the light source passing the object’s silhouette. In direct sunlight (parallel rays), the shadow edge runs parallel to the object’s contour projected onto the ground plane. The formula: shadow direction = light direction vector × object height. The length of cast shadow L = h / tan(θ), where h is object height and θ is the angle of the light source above horizontal.

光线在形体上的表现遵循可预测的几何关系。物体遮挡光线时会形成投射阴影；其边缘由光源射线经过物体轮廓所决定。在平行光（阳光）下，阴影边缘平行于物体轮廓在地面上的投影。公式：阴影方向 = 光线方向向量 × 物体高度。投射阴影长度 L = h / tan(θ)，其中 h 为物体高度，θ 为光线与水平面的夹角。

Form shadow (the dark side of an object) plus a core shadow and reflected light create the illusion of volume. The terminator line divides light and shadow; its softness depends on the size of the light source. Large source = soft transition.

形体阴影（物体的暗面）加上明暗交界线和反射光创造出体积错觉。明暗交界线分隔光与影；其柔和程度取决于光源大小。大光源 = 柔和的过渡。

11. Repetition, Rhythm & Pattern Formula | 重复、节奏与图案公式

Rhythm in visual art is created by repeating elements with variation. The simplest formula is a regular beat: identical shapes at equal intervals. More dynamic rhythms follow ratio progressions: 1, 2, 4, 8 (geometric) or 1, 1, 2, 3, 5 (Fibonacci growth, echoing φ). Pattern is the systematic repetition of a motif across a surface using one of four symmetry operations: translation, rotation (order 2, 3, 4, 6), reflection, and glide reflection.

视觉艺术中的节奏通过重复元素与变化来创造。最简单的公式是规律节拍：相同形状等距排列。更具动感的节奏遵循比例级数：1, 2, 4, 8（几何级数）或 1, 1, 2, 3, 5（斐波那契增长，呼应 φ）。图案则是通过四种对称操作将母题系统性地重复于表面之上：平移、旋转（2、3、4、6次）、反射和滑动反射。

Combining rhythms: overlapping a slow rhythm (large interval) with a fast rhythm (small interval) builds visual counterpoint, a principle central to textile design and abstract composition.

节奏组合：将慢节奏（大间隔）与快节奏（小间隔）叠加会构建视觉对位，这是纺织品设计和抽象构图的核心原则。

12. Canon of Proportions: The Human Figure | 比例标准：人体比例

The classical canon (idealised proportions) uses the head as a unit of measurement. In the Renaissance ideal, total height ≈ 7½ to 8 heads. Detailed landmarks: the halfway point of the body is the pubic bone; the elbow aligns with the waist; the hand reaches mid-thigh. For the face, the eyes are at the halfway mark of the head, the width of the eye fits five times across the face, and the corners of the mouth align with the pupils.

古典比例标准（理想化比例）以头长为度量单位。文艺复兴时期的理想比例中，全身高度 ≈ 7½ 至 8 头长。详细定点：身体的一半位于耻骨处；肘部与腰部齐平；手部下垂至大腿中部。面部方面，眼睛位于头部一半处，面部宽度是五只眼睛的宽度，嘴角与瞳孔对齐。

These proportional formulas can be deliberately distorted for expressive effect. El Greco elongated figures to 10–12 heads to convey spirituality, a purposeful deviation from the canon.

这些比例公式可以被有意地变形以达到表现效果。埃尔·格列柯将人物拉长至 10–12 头长以传达精神性，这是对比例标准的有意背离。

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AS WJEC Art: Formula & Theorem Quick Reference Guide | AS WJEC 艺术：公式定理速查手册